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An Experimental Investigation Of Heat Conduction Through Liquid-Liquid Phase Boundaries
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An Experimental Investigation Of Heat Conduction Through Liquid-Liquid Phase Boundaries
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T his d issertatio n has been 64— 2567 m ic ro film e d exactly as received C O O PER , H a rris o n Raymond, 1929- AN E X P E R IM E N T A L IN V E S T IG A T IO N O F H E A T C O N D U C TIO N THROUGH L IQ U ID - L IQ U ID PHASE BO UNDARIES. U n iv e rs ity of Southern C a lifo rn ia , P h .D ., 1963 Engineering, chem ical University Microfilms, Inc., Ann Arbor, Michigan AN EXPERIMENTAL INVESTIGATION OF HEAT CONDUCTION THROUGH LIQUID-LIQUID PHASE BOUNDARIES by Harrison Raymond Cooper A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (Chemical Engineering) June 1963 UNIVERSITY OF SO UTHERN CALIFO RNIA ORADUATK SCHOOL UNIVERSITY PARK LOS ANOSLKS 7. CALIFO RNIA This dissertation, written by Ha k xi h.qa. R 2y.m9.nd. . Q. v . ° p . < ? . r . ....... under the direction of A is....Dissertation C om mittee, and approved by all its members, has been presented to and accepted by the Graduate School, in partial fulfillm ent of requirements for the degree of D O C T O R O F P H I L O S O P H Y & ... D ate J.uae*..i.9.63................ DISSERTATION COMMITTEE ChMrm«* PLEASE NOTE: Figure pages tend to Mcurl" Filmed in best possible way UNIVERSITY MICROFILMS, INC. * ACKNOWLEDGMENT Financial assistance from the National Science Foun dation in the form of a Graduate Cooperative Fellowship (1961-1962) is hereby acknowledged. ii TABLE OF CONTENTS Page ACKNOWLEDGMENT..................................... ii LIST OF.T A B L E S ..................................... v LIST OF FIGURES..................................... vi Chapter I. SUMMARY OF THE EXPERIMENTAL INVESTIGATION............................ 1 Introduction Results Conclusions II. SURFACE DIFFUSION PROCESSES: THEORETICAL AND EXPERIMENTAL BACKGROUND............. 17 III. DESCRIPTION OF THE EXPERIMENTAL STUDY OF HEAT CONDUCTION THROUGH LIQUID-LIQUID INTERFACES............................... 24 IV. SIGNIFICANCE OF THE RESULTS............... 34 Interfacial Residuals Consideration of Measurement Error Thermal Conductivity of Mercury LIST OF REFERENCES................................. 43 APPENDIXES Appendix A. The Experimental Apparatus......... 47 Appendix B. The Experimental Procedure ......... 63 iii Page Appendix C. Analysis of the Data............... 75 Appendix D. Tabulation of Experimental Data . . 93 iv LIST OF TABLES Table Page 1. Summary of Interfacial Residuals from Two-Film Data.......................... 8 2. Summary of Regression Coefficients from Single Film D a t a ...................... 12 3. Summary of Regression Constants from Single Film D a t a ...................... 14 4. Thermal Conductivity Comparison ............. 40 5A-35B. Thermal Conductivity Cell Measure ments (A), Data Analysis (B)............... 95- 156 v LIST OF FIGURES Figure Page 1. Schematic Diagram of Heat Flow Apparatus ................................... 6 2. Scale Drawing of Heat Flow Apparatus......... 26 3. Details of Heat Conducting Bars and Thermocouple P i n s .......................... 30 vi CHAPTER I SUMMARY OF THE EXPERIMENTAL INVESTIGATION Introduction Experimental measurements of heat conduction through two immiscible liquid phases in series were made to investi gate the influence of a liquid-liquid interface on rates of heat conduction. Heat conduction rates were determined from temperature gradients through known thicknesses of liquid films on either side of the interface, observed under static conditions. Interfacial effects were evaluated by analysis of heat flow through the individual liquids from the liquid thermal conductivities since convective heat transfer did not occur. Engineering analysis of heat transfer applications is performed by considering only the heat transfer processes through continuous portions of the involved media. Influ ences of phase boundaries on the flow of heat are always considered negligible. It is assumed that any surface in fluence on heat transfer is small because such effects are 1 2 unnoticed in most technological applications. However, in high heat flux processes the possibility of a surface compo nent having a significant influence on heat transfer becomes interesting from a practical point of view. Convective heat transfer using liquid metal is a process in which coeffi cients of heat transfer range from 1000 to as high as 2000 BTU/(hr.)(sq.ft.)(°F.). The presence of a component of heat transmission due to surface phenomena was investigated from heat transfer resistances. Evidence for interfacial effects on heat transfer was evaluated by comparing the measured resistance to heat flow to the estimated resistance without the inter face. The difference between these two resistance quanti ties is a residual quantity representing the influence of the interface in the path of heat flow. The order of pre cision of experimental measurements was directed toward de tection of residual quantities that would be significant in analysis of applications employing high heat transfer. A high heat flux process employing liquid metal is carried out with convective thermal resistances as low as 0.0005 recip rocal units of the conventional heat transfer coefficient units, BTU/(hr.)(sq.ft.)(°F.). Although a solid-liquid interface is more directly 3 of interest in heat transfer applications than a liquid- liquid interface, the experimental difficulties in evaluat ing properties of a solid-liquid interface were sufficiently great to make investigation of the liquid-liquid phase in terface desirable for fundamental determination of the pro cess of heat flow across a phase boundary. First of all, the area of a liquid-liquid interface can be accurately de fined within molecular dimensions, while in contrast a solid surface area is indeterminable by ordinary means because of gross and microscopic roughness. Second, surface adsorption on a liquid phase boundary can be treated with fundamental thermodynamics, but adsorbed films on solid surfaces are composed of various molecular species such as oxides which strongly adhere to the surface by complex bonding mecha nisms . A previous experimental work has been published by Mizushima, Iuchi, Sasano, and Tamura in which investigation of the thermal resistance at the interface between copper and mercury was described (16). The technique used by the cited authors was measurement of residual resistances using temperature gradient data through mercury films between copper surfaces, a technique very similar to that employed in this investigation. The authors claimed the ability to 4 detect residual values of resistance in the range 0.00007 to 0.0002 reciprocal BTU/(hr.)(sq.ft.)(°F.), and drew the con clusion that heat transfer resistance due to the metal- liquid surface was insignificant. Results Figure 1 is a schematic diagram of the heat flow apparatus used for measuring thermal resistance of liquid films. The experimental measurements are thermocouple read ings from junctions inserted in steel bars, the surfaces of which contain the horizor.tal liquid films. In addition, the thicknesses of the films are measured. Thermocouples at the five fixed levels shown on Figure 1 are used in combinations to provide independent determinations of the heat flow rate through the film and the film thermal resistance. The rate of heat flow is proportional to the thermal gradient in the steel bar. The lower bar was made thick enough for accurate determination of the gradient, measured independently by differences in levels 3 and 4, and levels 3 and 5. Film resistances were obtained independently by thermocouple EMF differences between levels 1 and 4, and levels 2 and 3, each divided either by the 3-4 gradient or the 3-5 gradient. Resistances at several film thicknesses were determined for Figure 1. Schematic Diagram of Heat Flow Apparatus thermo couplo pint, annulus liquid somplo container loads to potontlomotor (typical) thermo couple pins HOT WATER CIRCULATION LEVEL 1 UPPER STEEL BAR LEVEL ? LIGHTER LIQUID FILM HEAVIER LIQUID FILM LEVEL 3 thermocouple Junctions (typical) LEVEL 4 LOWER STEEL BAR LEVEL 5 COLD WATER CIRCULATION FIGURE 1 SCHEMATIC DIAGRAM OF HEAT FLOW APPARATUS 7 each experiment in which haat flow across the liquid-liquid interface was measured in order to determine the accuracy of the residual estimate by analysis of covariance. The experimental data for residual quantities are summarized in Table 1. Each group of resistances determined for a fixed heavier liquid film thickness and variable lighter film thickness is designated as a set. Each resid ual value is given with 90 per cent confidence limits of its estimate based on statistical treatment of the experimental measurements. Three separate sets were measured for each of the four liquid-liquid systems chosen for study. The results of each set at the four independent measurement points, and three set results at each of the measurement points, were combined by a statistical treatment to form a pooled estimate of the residual which can be stated more precisely than the individual results. The four liquid-liquid systems employed in the analysis of heat conduction across liquid-liquid phase boundaries have characteristically different interfaces. The types of interfaces investigated were liquid metal-polar liquid (mercury-water), liquid metal-hydrocarbon (mercury- toluene), oxygenated organic liquid-hydrocarbon (glycerol- 8 TABLE 1 SUMMARY OF INTERFACIAL RESIDUALS FROM TWO-FILM DATA Residuals are resistances with equivalent inches of steel. To convert to resistance in units reciprocal of BTU/(hr.)(sq.ft.)(°F.), multiply by 3.0 (10-3). Mer cury-Water Set 1 2 3 Pooled Thickness of Heavier Film (inches) 0.1280 0.1280 0.1303 Range of Lighter Film Thickness (inches) 0.0145- 0.0545 0.0149- 0.0557 0.0108- 0.0508 3-5 Gradient Level 2-3 Level 1-4 -0.08*0.06 -0.02*0.09 -0.11*0.15 -0.06*0.16 -0.11*0.04 -0.08*0.04 -0.10*0.04 -0.04*0.05 3-4 Gradient Level 2-3 Level 1-4 -0.17*0.04 -0.14*0.06 -0.14*0.16 -0.14*0.16 -0.03*0.12 -0.01*0.11 -0.11*0.04 -0.10*0.05 Pooled -0.09*0.02 -0.11*0.07 -0.06*0.03 Mercury-Toluene Thickness of Heavier Film (inches) 0.1239 0.1300 0.1266 Range of Lighter Film Thickness (inches) 0.0187- 0.0483 0.0090- 0.0397 0.0113- 0.0414 9 TABLE 1— Continued Set 1 2 3 Pooled 3-5 Gradient Level 2-3 Level 1-4 -0.23*0.43 -0.12*0.44 -0.66*0.31 -0.61*0.33 -0.38*0.31 -0.24*0.33 -0.42*0.17 -0.31*0.17 3-4 Gradient Level 2-3 Level 1-4 -0.26*0.35 -0.23*0.37 -0.58*0.30 -0.58*0.30 -0.60*0.31 -0.57*0.31 -0.48*0.15 -0.46*0.16 Pooled -0.21*0.17 -0.61-0.15 -0.45*0.15 Glycerol-Toluene Thickness of Heavier Film (inches) 0.0441 0.0426 0.0621 Range of Lighter Film Thickness (inches) 0.0172- 0.0573 0.0134- 0.0583 0.0096- 0.0594 3-5 Gradient Level 2-3 Level 1-4 0.27*0.58 0.12*0.40 -0.14*0.81 -0.10*0.81 -0.01*0.56 -0.05*0.53 0.04*0.33 -0.01*0.29 3-4 Gradient Level 2-3 Level 1-4 0.40*0.36 0.38*0.36 -0.03*0.67 0.03*0.67 -0.30*0.52 -0.37*0.49 0.02*0.25 0.01*0.24 Pooled 0.29*0.17 -0.06*0.29 -0.18*0.19 Water-Nujol Thickness of Heavier Film (inches) 0.1105 0.0917 0.0849- 0.0912 10 TABLE 1— Continued Set 1 2 3 * Pooled Range of Lighter Film Thickness (inches) 0.0261- 0.0515 0.0353- 0.0575 0.0365- 0.0699 3-5 Gradient Level 2-3 Level 1-4 0.88-0.83 1.04-0.83 -0.92-0.42 - -0.71*0.41 - 0.08*0.63 0.06*0.68 -0.04*0.31 0.09*0.31 3-4 Gradient Level 2-3 Level 1-4 -0.55*1.23 -0.51*1.23 -1.25-0.52 -1.18-0.67 0.46*0.43 0.51*0.44 -0.45*0.38 -0.41*0.40 Pooled 0.21-0.41 -1.02-0.21 0.21*0.22 *Pooling between samples is not Therefore values are indicative only. statistically valid. toluene) , and polar liquid-hydrocarbon (water-Nujol1). Pooled residual values over all three sets for each of these systems are as follows: mercury-water -0.0003*0.0001 mer cury-toluene -0.0013*0.0004 glycerol-toluene 0.0001*0.0007 water--Nujol (see below)*0.0010 reciprocal units of BTU/(hr.)(sq.ft.)(°F.) ^-Nujol is a registered trademark of Plough, Inc. 11 The range of the 90 per cent confidence limits are smallest for the fluids having the highest thermal conductivities. For the water-Nujol system, two of the pooled sample resid uals were within 90 per cent confidence limits of the esti mate around zero, but one result was a negative value with a statistically significant deviation from the others. Com bination of the three into a pooled estimate is invalid. However, the simple average is within the confidence limits of the estimate. The resistance of the two-liquid films measured in heat flow apparatus were compared to the thermal resistance of the observed thicknesses of liquids calculated from data obtained with single films. Film resistance and film thick ness data were obtained in several data sets for each of the five individual liquids employed in the investigation of two-film resistances. The relationship between film re sistance and film thickness was found to be linear for all data sets, which verifies absence of heat transfer by con vection through the films. The results of regression anal ysis for the repeated data sets for individual liquids are given in Table 2 and Table 3, with 90 per cent confidence limits of the regression analysis given for each value of regression coefficient and regression constant. TABLE 2 SUMMARY OF REGRESSION COEFFICIENTS FROM SINGLE FILM DATA Units of regression coefficient: dimension!.ess, the ratio of liquid thermal resistance per unit of length to steel thermal resistance per unit of length of liquid (the inverse ratio of steel thermal conduc tivity to liquid thermal conductivity). 3-5 Gradient Set Water Toluene Mercury Nu jol Glycerol 1 76.8*1.1 381.8*29.3 6.09*0.19 383.2*7.2 169.6*1.0 2 78.1*1.4 381.7* 6.7 6.09*0.08 384.8*6.9 169.7*2.7 3 78.9*2.2 377.4* 6.9 5.95*0.48 385.4*7.3 Z— 6 4 77.0*0.5 364.7* 5.7 6.01*0.14 381.2*5.6 5 6.13*0.44 Pooled 77.2*0.5 374.8* 4.8 6.05*0.09 383.8*4.3 169.6*1.0 1 76.8*1.1 382.2*30.4 5.75*0.26 383.1*7.4 169.7*1.3 2 78.1*1.2 381.9* 6.2 5.93*0.10 384.8*7.0 169.7*2.8 Level 3 79.0*2.0 377.9* 7.5 5.89*0.31 385.5*7.7 1-4 4 77.0*0.6 364.8* 5.5 5.83*0.16 381.6*5.5 5 5.92*0.27 Pooled 77.2*0.5 375.0* 5.0 5.86*0.07 383.6*3.0 169.7*1.0 £ TABLE 2— Continued 3-4 Gradient Set Water Toluene Mercury Nu jol Glycerol 1 75.5-1.7 373.1*25.9 6.33*0.29 378.1*7.6 164.8*1.1 2 76.7*1.5 371.0* 8.2 6.53*0.15 379.8*6.4 168.9*3.0 Iicvcl 3 77.9-2.7 367.6* 5.1 6.12*0.69 373.0*7.2 2—3 4 76.0*0.6 361.7* 6.6 6.11*0.26 370.9*6.5 5 6.20*0.53 Pooled 75.9*0.6 367.4* 3.9 6.29*0.14 375.6*3.7 166.5*1.5 1 75.5*1.8 373.2*26.1 6.35*0.33 378.0*7.8 165.0*1.3 2 76.6*1.4 371.1* 8.2 6.59*0.21 379.8*6.4 167.9*3.1 Level 3 78.0*2.8 376.6* 4.9 6.06*0.77 373.0*7.5 1-4 4 76.0*0.6 361.7* 6.5 6.08*0.20 370.9*6.3 5 6.04*0.50 Pooled 75.9*0.6 367.4* 4.1 6.28*0.16 375.6*3.3 166.6*1.5 TABLE 3 SUMMARY OF REGRESSION CONSTANTS FROM SINGLE FILM DATA Units of regression constant: inches of steel. To convert to resistance in units reciprocal of BTU/(hr.)(sq.ft.)(°F.), multiply by 3.0 (10“**). 3-5 Gradient Set Water Toluene Mercury Nu jol Glycerol 1 1.02-0.11 0.96*0.60 1.02*0.02 1.28*0.29 0.99*0.05 Level 2 3 1.03*0.06 1.05*0.05 1.16*0.13 1.03*0.14 1.10*0.01 1.08*0.03 1.62*0.40 0.93*0.25 0.89*0.18 4 5 0.98*0.04 1.36*0.25 1.03*0.01 1.00*0.04 1.10*0.18 Pooled 1.02-0.03 1.11*0.13 1.05*0.01 1.24*0.18 0.95*0.06 1 3.21*0.11 3.13*0.62 3.18*0.02 3.48*0.29 3.18*0.06 Level 2 3.16*0.05 3.35*0.13 3.18*0.01 3.77*0.40 3.06*0.18 3 3.20*0.05 3.22*0.15 3.16*0.02 3.07*0.26 1-4 4 5 3.16*0.04 3.54*0.24 3.16*0.01 3.14*0.02 3.23*0.18 Pooled 3.19*0.03 3.29*0.13 3.16*0.01 3.43*0.07 3.13*0.13 TABLE 3— Continued 3-4 Gradient Set Water Toluene Mercury Nu jol Glycerol 1 1.03*0.17 0.96*0.53 1.00*0.03 1.28*0.30 0.96*0.05 Level 2 1.0^0. 07 1.14*0.16 1.14*0.01 1.58*0.36 0.89*0.20 3 1.03*0.06 1.05*0.10 1.10-0.04 0.94*0.25 2-3 4 5 0.97*0.04 1.38*0.28 1.02*0.02 1.00*0.04 1.17*0.21 Pooled 1.02*0.04 1.12*0.10 1.05*0.01 1.31*0.09 0.93*0.16 1 3.19*0.18 3.09*0.54 3.13*0.03 3.45*0.31 3.09*0.06 Level 2 3.10*0.06 3.28*0.16 3.28*0.02 3.70*0.37 3.04*0.21 3 3.16*0.07 3.20*0.10 3.23*0.05 3.03*0.26 1-4 4 5 3.12*0.05 3.54*0.29 3.15*0.02 3.15*0.04 3.28*0.21 Pooled 3.16*0.04 3.26*0.11 3.19*0.01 3.43*0.09 3.07*0.14 16 Conclusions The interface of the water-Nujol system had no meas ured effect upon conductive heat transfer. The 90 per cent confidence limits of this measurement was - 0.0010 recipro cal units of BTU/(hr.)(sq.ft.)(°F.). The interface of the glycerol-toluene system also had no measurable effect upon conductive heat transfer, within the accuracy of measurements denoted by confidence limits of * 0.0007 reciprocal units of BTU/(hr.) (sq. ft. ) (° F. ). The interface of the water-mercury system caused a small increase in the measured rate of heat conduction which could not be accounted for in error analysis. The increase in heat conduction corresponded to a decrease in thermal re sistance of 0.0003 reciprocal units of BTU/{hr.)(sq.ft.) (°F.). The 90 per cent confidence limits of this value are a . - 0.0001 in the same units. The interface of the mercury-toluene system also caused an increase in the rate of heat transfer across the two films in series. The increase corresponds to a value of 0.0013 with 90 per cent confidence limits of * 0.0004 reciprocal units of BTU/(hr.)(sq.ft.)(°F.). CHAPTER II SURFACE DIFFUSION PROCESSES: THEORETICAL AND EXPERIMENTAL BACKGROUND The possibility of a surface resistance to heat transfer has received attention partly because clear exam ples have been found for mass transfer resistance at phase boundaries. In addition, discrepancies have been noted in heat transfer data which could be explained by presence of a boundary heat transfer resistance. Although the rates of heat and mass diffusion pro cesses are linear with potential gradients and thus proceed in an analogous fashion, the coefficients which describe these processes are each determined by different physical principles. The mechanisms of heat and mass transport in a liquid phase are determined, and related to one another, by the tendency of individual molecules to be restrained with in relatively mobile clusters (15). Whereas heat diffusion can proceed by impact transport and translation transport (free flight), mass diffusion can only take place by 17 18 translation (7). This behavior is reflected by the obser vation that thermal conductivity coefficients increase with increasing density, as can occur either by decreasing tem perature or increasing pressure, while mass diffusion co efficients diminish. An increase in thermal conductivity also results from increasing molecular orientation. Therm al conductivities of a solid phase are always substantially greater than the same substance in its liquid phase. For example, thermal conductivity of ice is about three times that of water, although the density of ice is 10 per cent less than water. The molecular environment at a liquid phase boun dary is altered from the bulk state by surface forces which are the basis for the Gibbs adsorption at an interface. In addition to adsorption, molecular properties at an inter face are subject to orientation forces. Hennicker has de scribed phenomenological evidence of long range forces be tween molecules which result in orientation at liquid sur faces up to depths of hundreds of molecular diameters (9). Further evidence of long range intermolecular forces has more recently been reviewed (1). The differences in molec ular environment between bulk and surface states brought about by adsorption and intermolecular forces can cause changes in the transport mechanisms. If the impact trans port mode is augmented to a greater extent than the trans lation mode is diminished, the result will be an increase in heat diffusion accompanied by a decrease in mass diffu sion at the interface. There is a significant possibility that these factors may account for the decreased diffusion of heat observed in the films containing liquid-liquid in terfaces . A boundary mass transfer resistance has been exper imentally documented for three types of diffusion across a liquid interface. These cases are of interest because of the theoretical interaction between mechanisms of heat and mass transport. The most significant evidence of boundary resistance to mass diffusion is the case of reduced evapor ation of water due to monomolecular films of certain long chain hydrocarbon derivatives on the surface of the water (19). Single molecular thicknesses of these materials, ar ranged in dense orientations on the water surface, sharply reduce diffusion of water molecules across the interface. A second case of interfacial diffusion resistance at a liquid phase boundary is related to free evaporation from surfaces. It has been proposed that a given liquid surface without detectable impurities has a maximum rate of 20 evaporation below the rate theoretically possible. The re duction ratio, called the accomodation coefficient, has been investigated several times and is claimed to be a fun damental quantity specific to each liquid (9). Evaporation from free surfaces has also been explored from the point of view that any reduction from the theoretical rate is the result of mass transfer inhibition due to minute quantities of random adsorbed impurities (11,12). A final case in which evidence is shown for diffu sion resistance at liquid phase boundaries results from the experimental work of Drickamer and co-workers (22,23). These experiments were designed to determine resistance to mass diffusion through liquid-liquid phase boundaries under static conditions. Evidence of a static interfacial resist ance was found using radioactive isotopes to measure rates of mass diffusion across liquid-liquid interfaces. Mechanisms have been proposed to explain experi mental findings of mass transfer diffusion resistance at a liquid interface. Reduced evaporation rates through a dense monomolecular film has been treated from a fundamental standpoint by La Mer (19). The reduced rate of mass diffu sion across the film is described as the result of an ener gy barrier. Only the fraction of water molecules possessing 21 an escape energy above a certain limit at a given time can pass through the interface, this limit being at a higher level than required for free evaporation. The concept of an energy barrier has been extended to form a theoretical basis for the fundamental accomodation coefficient based on altered energy states of molecules at the liquid surface. Finally, Drickamer noted a relationship between occurrence of an interfacial diffusion resistance and a tendency toward hydrogen bonding between components in the observed liquid systems. The mechanisms proposed for reduced mass diffusion rates at an interface imply an increase in molecular density or orientation. The finding of this investigation that an incremental increase in thermal conductivity may occur at a liquid-liquid phase boundary is supported by evidence for diffusion resistance across the interface, if the decrease in diffusion rates is due to increased density or orienta tion of molecules. Although the likelihood of a resistance to heat transfer at phase boundaries is diminished by consideration of the theoretical basis, several instances of apparent boundary resistance to heat transfer have been discussed in the literature. Surface resistances have been offered as 22 an explanation for discrepancies in data for liquid metal heat transfer using NaK (2). In another review of convec tive heat transfer data with liquid metals, differences have been rationalized on a basis of "wetting" and "non-wetting" of metal walls by the liquid, a factor related to a surface characteristic (14). Residual heat transfer resistances at the interface of two metal surfaces in contact have been measured using gradient analysis by different investigators employing var ious techniques to attempt reduction of residual resistances and to explain by mathematical treatment the presence of significant residual resistances. In spite of technical sophistication of experimental techniques and mathematical analysis, residual resistances of appreciable size are dif ficult to explain. For example, poor correlation is ob served between residual resistance values obtained in air or vacuum and those obtained after submerging the contacting surfaces in better conducting fluids such as glycerol (3,6). A final citation of apparent surface heat transfer resistance is the case of the interfacial resistance between liquid helium II and metal which occurs below 2° K. and is therefore only of academic interest at this time. This well documented interfacial resistance becomes appreciable; at 23 0.4° K. the reported value is 1.0 in reciprocal units of BTU/(hr.)(sq.ft.)(°F.) (13). It has been noted that the Lyons theoretical equa tion for predicting liquid metal convection coefficients has been successful in correlating data for most liquid met als, but for a few metals (especially mercury) the correla tion predicts consistently higher coefficients than have been observed. This fact has been cited as possible evi dence for an interfacial heat transfer resistance between mercury and metal pipe walls. However, the discrepancy for mercury heat transfer data may be accounted for if data for mercury thermal conductivities used in determining the pre diction are incorrectly high, as apparently is the case on the basis of data obtained in this investigation (see this text, p. 40). CHAPTER III DESCRIPTION OF THE EXPERIMENTAL STUDY OF HEAT CONDUCTION THROUGH LIQUID-LIQUID INTERFACES Heat conduction experiments were carried out in an apparatus modeled after the thermoconductrimetric apparatus described by Sakiadis and Coates (20,21). The principle design change was substitution of a thin walled glass ring 0.75 inches high for sample containment in place of the heavy walled pyrex pipe used in the previous work. This change was feasible since the liquids used in the study were not highly volatile. Figure 2 shows the heat flow apparatus in which the two cylindrical steel bars of 6.00 inch diameter are the principal elements. The surfaces of the bars in contact with the sample were highly finished by surface grinding, machine lapping, plating by the chemical nickel process, and finally hand lapping. The upper bar, 1.25 inches thick, is positioned above the lower, 5.00 inches thick, by three Figure 2. Scale Drawing of Heat Flow Apparatus uppar bar leveling sc roar Ih riK M run tor uppar bar lovalini tcra* r t yh o t v ilt r Inlet v stainless itaal anvil hot mater locket outor Insulation an) rlne mount 37 ring nou n i"1 Ipofyacrylate plastic) thormal guard hoallng tapo support column l C"_? I ------ f+ :i r cold water In tat cold mater outlat apparatus leveling screm FIGURE 2 SCALE D R A W IN G OF HEAT FLO W APPARATUS 27 leveling screws acting against support columns. The sample film is placed in the space between the two bars. The two steel surfaces are made parallel by adjusting the distance between the bottom free standing position and the measure ment position with the leveling screws in conjunction with readings of three micrometers calibrated to 0.0001 inch. Steady state temperature gradients through the bars are achieved by contacting the ends of the bars with circu lating water from hot and cold constant temperature surge tanks controlled to -0.01°F. Pumps circulate the water at a rate sufficiently high to result in negligible temperature change of the contacting water passing through the cell. Hot water at approximately 130°F. is supplied to the top bar to conduct heat from top to bottom through the film and thereby avoid convection. The cold water temperature was maintained at 80°F. Under these conditions the average film temperature varied between 110-120°F. Lateral heat losses were prevented by providing insulation around the cell to gether with heating tapes to hold the average temperature in the insulation slightly higher than the temperature in the lower steel bar. Temperature measurements were made with a Leeds and Northrup K-3 potentiometer and D-C null detector from 21 28 copper-constantan thermocouple junctions (30 gauge B&S) in serted in the upper and lower steel bars. With proper guarding of the measuring circuits, it was possible to con sistently reproduce EMF readings at steady state within 0.01°P. after 20-30 minute intervals. The thermocouple junctions were mounted in five 0.25 inch diameter steel pins driven into slightly undersized straight holes drilled on diameters of the steel bar by the gun-drilling process. Figure 3 shows a diagram of the bars indicating design of the pins and locations of the holes for insertion of the pins. Two pins are located in the upper bar and three in the lower to provide two independent determinations for the temperature gradients and two for the thermal resistances of liquid films between the steel surfaces in order to ob tain four sets of data for each sample determination to evaluate systematic error associated with thermocouple measurement. Samples of liquid were placed in the cell using techniques which eliminated air from the film of liquid be tween the steel surfaces. The maximum sample thickness var ied from 0.0600-0.1200 inches for single liquid films. Double films were thicker because of minimum thickness re quirements necessary to maintain a stable film on the Figure 3. Details of Heat Conducting Bars and Thermocouple Pins U P P E R O A R 400 I nch t oMMto r to m a t o r totiratonto < r c tost onc* rrM M iflM In cmtort •W tM N fiH (Inchti) LOO LOV tvs a « o f l = a O O O I n c h toimtor «un-0r1 IM nw iipvpw iiinniQ pK ip 1710 Indus UMR O A R 400 I nch to m itor toitonM Itm M rtan In cm M W ^Nii w / toMMtor to btothtoiclrcli asoo 10V ■ NbtoOmlM 1 0 op term lSVInch«IO-Ni lOapicmn) noMooounc pin (ntotoKtoto pint In iirto i In b in totrtont J u n c tto n m iMi t o pi n ctowft to wrfKi In cantoctvNhtoft HpuU L O O I nch ( t ypical) r * 1 L _ J B _ 4 ]IU-.MI. - -UII UlC^yj © ■ “---------* **■ * —* - - u * - ----* - '"n ^ ^ QQ I t O Incti w W O t to Mdi ttM nim upIt Into a OOO l-a OOOHndi w in l» 40V I nch toMMtor Kcmhtoifrm tltotopln H irfM aOVInch mIIM ilto FIGURE S D E S IG N D ETA ILS OF HEAT C O N D U C TIN G BA RS 31 surface of the lower bar. Double film thicknesses varied in the range 0.1000-0.1600 inches. The maximum thickness was determined by loss of accuracy due to large film resistan ces, which cause gradients to be reduced to the point that the limiting error of thermocouple measurement becomes sig nificant. To assure uniform thickness of the lower films when measuring double film samples, the lower bar was accur ately leveled with a 5.5 inch precision level to obtain a maximum deviation of about 0.00015 inch over the diameter of the bar. Resistance values were determined at four to seven film thicknesses for each single liquid data set to obtain the regression coefficient and regression constant results given in Tables 2 and 3. Replicate regression data for each single fluid were shown to be statistically equivalent, which permitted pooling of results for improved accuracy of the regression parameter estimates. Independent evaluation of regression variance from measurement error data produced good agreement with regression variance of experimental re sistance values, indicating validity of assuming linearity between film resistance and film thickness. Film thicknesses were measured directly using a microscope fixed in a micrometer slide cathetometer on a portable base which was positioned at the cell for each set of readings. The micrometer reads directly in 0.0001 inch on a vernier scale. Measurements of film thicknesses were made by back lighting through the film to the microscope field. Three film thickness measurements were read at each of three randomly selected positions of the cathetometer in order to minimize the influence of error due to light dif fraction through the glass containment ring. The standard deviation of the thickness measurement, as determined by analysis of cathetometer data, is approximately 0.00005 inch for values averaged from nine observations. The choice of liquids used in the two-film samples was limited by difficulty with stabilizing thin layers of liquids in thicknesses of 0.0500-0.1000 inch over the ex panse of the 6.00 inch diameter film surface. The liquid pairs chosen for study had very small mutual solubilities with the possible exception of glycerol-toluene. Samples of each liquid were obtained from standard sources at the highest purities commercially available with no attempt to further improve their purities. Since thermal conductivi ties of poor conducting liquids such as organic liquids are relatively insensitive to small amounts of impurities, es pecially if the impurities are chemicals of similar species, variability of impurity content within specification limits is unlikely to introduce measurable error. In the case of water and glycerol, trace additions of surfactants and dyes were used to improve the experimental technique. Mercury determinations were made with a supply taken initially from freshly distilled sources. Contaminating material in mer cury was removed after each test by filtering the recovered supply through a pin hole puncture in a filter paper cone. The mercury surface remained bright during the tests, indi cating that the impurity content remained very low (25). Statistical analysis combining data sets for each of the liquids showed only random differences among the sets based on measurements with liquids in their original states, with additives, and after equilibrium saturation with the other components of double films. CHAPTER IV SIGNIFICANCE OF THE RESULTS Interfacial Residuals The results of the tests for interfacial residuals given in Table 1 show that all mercury-water and mercury- toluene samples produced a significantly negative value. The mercury-water results are proportionately more dispersed than mercury-toluene results, but combined data for both systems are within the limits of 95 per cent significance tests for variance. Individual set results from pooled measurements with the glycerol-toluene system include one significant positive residual. Testing for significance between samples shows no cause for assuming differences. The pooled sample resid uals, as well as pooled results from the same independent measurements for three sets, all are within the confidence limits of the estimate around zero. No explanation could be found for the wide deviation of one of the water-Nujol data sets. The possibility that 34 35 aging of the interface may influence the thermal resistance of an interface was examined by collecting data over a 48 hour period from an undisturbed water-Nujol double film. The observed resistance did not change appreciably during the time test. Consideration of Measurement Error Random errors of measurement result from limits of precision for thermocouple EMF and film thickness measure ments. Consistent errors associated with a single set of data include errors from incorrect alignment of horizontal surfaces containing the film when carried through the se quence of runs in a data set. Errors of these two types are found through analyzing repetitive data. Systematic errors in the measurement technique are heat leakage through insulation and the liquid annulus, interference with grad ients as a result of heat input from thermal guarding, and consistent deviation of thermocouple measurements. If these sources of disturbances are small, the result will be a lin ear displacement of measurement variables. Small linear disturbances imposed on the linear relationships for compar ing data in the determination of residuals can be tolerated. Systematic non-linear thermocouple errors are de 36 tectable from analysis of data using the independent grad ient and film resistance data. Examination of regression data in Table 2 discloses an almost constant difference be tween regression coefficients from the two gradient esti mates, excepting the data for mercury (see p. 40). The dis placement between means varied from 1.7 per cent to 2.1 per cent, roughly increasing with increasing values of regres sion coefficients. The difference between results from the two gradients can be due to incorrect evaluation of the re sistance between thermocouple levels. Any disturbances caused by voids in the bars for leads to thermocouple junc tions or voids due to imperfect fitting of the thermocouple pins could result in systematic differences. Independent measurements of film resistance were equivalent for each gradient evaluation, which is evidence of negligible error due to thermal guarding as well as ab sence of systematic differences between steel temperatures at the thermocouple levels. The problem of thermal guarding was investigated further because adjustment of thermal guard heat is regarded as critical during measurement of thermal conductivities. In particular, the possibility of error due to improper thermal guarding for the Sakiadis-Coates thermal conductivity cell has been discussed in the literature (4). 37 The thermal guard utilized for this heat conduction appara tus was designed to prevent heat losses only from the lower bar where gradients are determined. Protection against lat eral losses in the upper bar was provided by shielding in sulation only. The risk of significant disturbance to grad ients due to heat losses from the upper bar is minimized by the diameter to thickness ratio of 4.5:1. Hot water temper atures, maintained at 130°F. maximum to decrease heat losses through the insulation, diminished the possibility of appre ciable lateral losses of heat in the upper bar between ther mocouple levels 1 and 2. Any significant loss of heat be tween these levels would be reflected by differences in re sistance between the levels proportional to the upper bar temperature. Systematic error of this type would be noted by a difference in regression coefficient in using levels 1 and 4 resistances vs. levels 2 and 3. Significant differ ences were not observed in the computed regression coeffi cients with either gradient. Thermal guarding of the lower bar, carried out with heating tapes surrounding a thickness of 1.5 inches of poly urethane foam insulation on the steel and covered with two inches of polystyrene foam, maintained an average tempera ture ranging from 4-8°F. between the steel surface and a 38 thermocouple level one inch from the steel in the insula tion. The possibility of disturbance in thermal gradients along the lower bar due to heat input from the thermal guard was considered, although calculations indicated heat input could be only as great as 0.3-0.5 per cent of heat flow through the bar at the smallest temperature gradients em ployed. To test the effect of this disturbance, Set 3 of the Nujol data was obtained with 2°F. thermal guard differ ence and Set 4 with 10°F. The disturbance caused by the difference in heat flow into the bar did not result in any statistical difference in the data. Further investigation of error sources due to heat leakage was conducted by simulating steady state operation of the thermal conductivity cell with a temperature gradient calculation programmed for a digital computer.^ The simula tion provided for cylindrical symmetry with regions of dif ferent thermal conductivity in a constant temperature sur rounding. Analysis showed a source of error in the Sakia- dis-Coates study was heat bypassing the liquid film through 1The computations were performed on the Honeywell 800 digital computer at the University of Southern Califor nia Computer Sciences Center. Assistance from staff person nel of the Minneapolis-Honeywell Corporation and the Univer sity of Southern California Computer Sciences Center is gratefully acknowledged. 39 the heavy walled pyrex pipe surrounding the steel bars. The apparent resistance of the liquid film decreases about 5 per cent as a result of heat bypass and the proportion of heat loss is nonlinear with the thickness of film. This degree of discrepancy due to incorrect estimate of heat flow through the film resolves differences in liquid thermal con ductivity data reported by Sakiadis and Coates on one hand, and Riedel and Powell on the other hand (21,18,4). Compu tations based on the apparatus modifications employed in this work determined leakage through the thin glass ring and annulus between the ring and steel bar to be small (less than one per cent) and linear with thickness. Thermal Conductivity of Mercury Thermal conductivity values given in Table 4 were calculated from pooled regression coefficients by compari son to toluene, using the thermal conductivity of toluene recently published as a standard (26). Good agreement is shown between reliable literature values and the average of four independent regression coefficient values relative to toluene for glycerol and water, but the mercury result is about 15 per cent less than the most widely accepted liter ature value at room temperature (Hall, 1938) (8,24). 40 TABLE 4 THERMAL CONDUCTIVITY COMPARISON Average Regression Coefficient from Pooled Data Thermal Conductivity Value BTU/(hr.)(ft.)(°F.) Measured Literature Reference Water Toluene Mercury Nu jol 6.12 4.48 379.60 0.0721 168.10 0.163 76.50 0.358 371.10 0.0738 0.367 basis 5.45 (17) (26) (8) Glycerol 0.165 (18) Ewing, et al. recently measured mercury thermal conductivi ty at elevated temperatures (above 300°F.) and also deter mined values about 15 per cent lower than previously found by Hall (5). In view of the findings reported here, it ap pears the thermal conductivity of mercury at room tempera ture may also be considerably lower than previously accept- Regression data for mercury were more sensitive to systematic error than the other liquids examined because even up to the maximum film thicknesses of 0.12 inches the mercury film resistances were very low. Systematic error in thermocouple measurements therefore have proportionately ed 41 greater influence on the results. In addition, thermocouple corrections could not be determined to adjust the gradient and resistance calculations because of insufficient accuracy of a zero gradient estimate by linear regression of thermo couple readings with gradient calculations using a narrow range of gradient estimates. Regression coefficients de rived from the two independent gradients differ by approx imately 6.5 per cent after allowing for differences between gradients in the data for the remaining liquids. Since annular bypass of heat in mercury can be more appreciable than in poorly conducting fluids, the analysis published by Mizushima, et al. for approximate calculation of heat flow around cylindrical bars with an annular space was employed to evaluate this source of error (16). The annular heat bypass is judged to be less than one per cent, and an error from this source would result in a higher value than the true thermal conductivity. LIST OP R E FE R EN C ES LIST OF REFERENCES 1. Adamson, A. W., "Physical Chemistry of Surfaces," Interscience, New York(1960). 2. Astakhov, O. P, Petrov, V. I., Fedynskii, O. S., Atom- naya Energiia JL1, 255 (1961). 3. Cetenkale, T. N., Fishenden, M., International Confer ence on Heat Transfer, Institution of Mechanical Engineers, London(1951). 4. Challoner, A. R., Powell, R. W., Proc. Roy. Soc. (Lon don) A238. 90 (1956). 5. Ewing, C. T., Seebold, R. E., Grand, J. A., Miller, R. R., Naval Research Laboratory Report 4506, March 17, 1955 (Washington, D. C.). 6. Fenech, H., Rohsenow, W. M., Atomic Energy Commission Report NYO-2136. May 1959 (Washington, D. C.). 7. Franck, E. U., Jost, W., Z. Elektrochem. 62,, 1054 (1958). 8. Hall, W. C., Physical Review JS3, 1004 (1938). 9. Heideger, W. J. , Boudart, M., Chem. Eng. Sci. 1 7 ., 1 (1962). 10. Henniker, J. C., Rev. Modern Physics j21, 322 (1949). 11. Hickman, K. C. D., Ind. Eng. Chem. 46, 1442 (1954). 12. Hickman, K. C. D., Torpey, W. A., Ind. Eng. Chem. 46, 1446 (1954). 13. Lee, D. M., Fairbank, H. A., Phys. Rev. 116, 1359 (1959). 43 44 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. MacDonald, W. C., Quittendon, R. C., Chem. Eng. Prog ress Symposium Series No. 9, J30, 59 (1954). Mizushima, S., Proc. Fujihara Mem. Fac. Eng., Keio Univ., 8, No. 28, 7 (1955). Mizushima, T., Iuchi, S., Sasano, T., Tamura, H., Int. J. Heat Mass Transfer .1, 139 (1960). Powell, R. W., Challoner, A. R., Phil. Mag., Ser. 8, 4, 1183 (1959). Riedel, L., Chem. Ing. Tech. 2 3 465 (1951). Rosano, H. L., La Mer, V. K. , J, Phys. Chem. 60, 348 (1956). Sakiadis, B. C., Coates, J., Eng. Exp. St. Bulletin No. 45, Louisiana State University, Baton Rouge, La., (1954). Sakiadis, B. C., Coates, J., A. I. Ch. E. J. JL, 275 (1955) . Sinfelt, J. H., Drickamer, H. G., J. Chem. Phys. 23. 1095 (1955). Tung, L. H., Drickamer, H. G., J. Chem. Phys. 20, 6 (1952) . U. S. Atomic Energy Commission, Liquid-Meta 1 s Handbook, Washington, D. C. (2nd ed., June, 1952). Wichers, E., Chem. Eng. News 20_, No. 17, 1111 (1942). Zeibland, H., Int. J. Heat Mass Transfer 2, 273 (1961). A P P E N D I X E S APPENDIX A THE EXPERIMENTAL APPARATUS APPENDIX A THE EXPERIMENTAL APPARATUS The key elements of the experimental apparatus used in this research are the heat flow apparatus, the tempera ture controlled hot and cold water reservoirs with circulat ing pumps, and the potentiometer used for measurement of thermocouple EMF's. The Heat Flow Apparatus1 Design and fabrication of the steel bars.— The steel bars are approximately six inches in diameter. The upper bar is approximately 1.25 inches in thickness and contains two thermocouple levels each having four junctions. The lower bar is about five inches thick and contains three thermocouple levels, two of which have four and the other lfrhe author is indebted to Dr. Harold Rodriquez, then doing graduate research at Louisiana State University, for his comments and advice based on the design of the par allel plate thermal conductivity cell used in their re search. The author thus benefited by experience gained from previous experimental work done with this type of apparatus. 47 48 five junctions. The steel used for machining the upper and lower bars was obtained from the Ducommun Company in Los Angeles from selected hot rolled, normalized mild steel stock 6 1/2 inches in diameter. Ultrasonic tests on seven and eight inch lengths of this stock, performed by the Mag- naflux Corporation in Los Angeles, indicated no detectable voids or inclusions. An ultrasonic test at high gain on a two inch thickness indicated no detectable grain size dif ferences along the diameters of the test piece. The cylindrical surfaces of the bars were prepared by the San Val Tool and Die Company, Sun Valley, California, by machining them to rough size followed by grinding to a diameter tolerance of 0.0005 inch. The top and bottom sur faces of each bar were made square and parallel by surface grinding. After completion of machining and grinding, the surfaces to be in contact with the liquid samples were machine lapped to a smooth finish on facilities furnished by the Byron Jackson Mechanical Seal Division of the Borg- Warner Corporation. The bars were then plated by the Kani- gen process^ with a thickness of nickel approximately 0.0006 inch on all surfaces. The Kanigen process deposits ^Kanigen is a registered trade mark of the General American Transportation Company. 49 a film with negligible build-up on edges and surface discon tinuities. Following the plating process the smooth sur faces were hand lapped using fine lapping compound furnished by Byron Jackson. Thermocouple preparation and insertion.— The therm ocouples were mounted in 0.25 inch diameter steel pins which were driven into holes drilled through the bar on the different diameters shown in Figure 3. The holes for the pins were made by the "gun-drilling" process to insure straight bores. Although the straightness of gun-drilled holes is assured, it is not certain in a given case that a close tolerance can be held for parallelness of the holes. For this work, dimensional measurements on the finished bars showed that the top of the gun-drilled holes was the same distance from the lapped surface at either end within 0.001 inch tolerance. The thermocouple pins were made from 0.25 inch over size mild steel rod. The pins were undercut approximately 0.001 inch on diameter except at thermocouple lands, where the stock remained oversize by approximately 0.0001 to 0.0002 inch as measured by hand micrometer. The pins were grooved with a 0.030 by 0.040 inch rectangular slot dimen- 50 sion along their length with a milling tool for thermocouple wire access. At each thermocouple land, a 0.040 inch hole was drilled to the surface of the pin from the groove. The thermocouple wires, cotton wrapped enamelled 30 gauge B&S copper-constantan (Leeds and Northrup catalogue 30-55-3), were cemented into the holes with epoxy cement. The junc tions were prepared by trimming the wires flush with the steel surface followed by forming a film of solder across the steel and thermocouple wire with rosin core solder. Care was taken to form the junction at the immediate surface of the steel by using an auxiliary potentiometer to monitor the junction preparation and by inspecting the junction under magnification after refinishing the steel surface with fine crocus cloth. In spite of precautions taken during preparation of the junctions and placement of the pins, a total of four thermocouples were lost in the insertion pro cess. Before insertion of the pins into the bars the radial relationships of the junctions on the pin surfaces were measured. Deviation from parallel relationship resulted from drift during drilling of the thermocouple holes with fine twist drills. Three thermocouple wires were brought out each end of the slotted pins. Including the cotton insulation, three 51 0.010 inch diameter wires at each emergent end of the pins nearly filled the slot. Voids in the slot where there were fewer wires were filled with a one to one mixture of petro latum and crystalline graphite to diminish thermal resist ance. The thermocouple pins prepared in this way were lub ricated on the contacting surface with a white lead-machine oil mixture and tapped into place with a plastic mallet. Even though the pins were placed in the holes by careful tapping, some degree of rotational movement of the pins oc curred which resulted in the displacement of the axis of the thermocouple holes in the pins from normal to the film surface. The radial movement was probably caused by fine helical surface irregularities in the holes remaining from the tool action in the gun-drilling process. The position of each junction in the bar, accounting for both nonparallel holes and deviation of the pin axis from normal to the sur face, was ascertained by scratching the end of each pin with a reference mark, noting the position of each junction in relation to the reference mark, and then measuring the position of the reference mark after the pin was driven into place. The sample containment and measurement.— The pyrex 52 glass ring containing the sample is approximately 3/4 inches higher than the surface of the lower bar. The ring is cem ented in epoxy to an acrylic plastic holder shrunk around the bottom bar about 1/8 inch below the top surface of the bars. This arrangement is shown in Figure 1. The annular gap between the glass ring and the 0. D. of the bar, about 1/8 inch, is filled with epoxy plastic almost to the surface of the bar. The top bar, suspended from steel support col umns shown in Figure 2, dips into liquid placed in the glass container. It is possible to visually observe through the glass ring while air bubbles are displaced from the sample between the top and bottom bars. Liquid samples are added and withdrawn from the sample using hypodermic syringe needles. The thickness of the sample is determined by optical measurement of the distance between the bars after adjusting the position of the top bar above the bottom bar with level ing screws moving in thread runs attached to a plate forming the top of the hot water jacket. Three micrometer heads are also attached to the plate in order to establish parallel surfaces. Parallel positioning of the bars is achieved by first reading the micrometers in a bottomed position (the parallel surfaces in free contact). When the bar is 53 elevated a desired amount by means of the leveling screws, adjustments are made in the screws until the difference in micrometer reading is the same for all three. The differ ences in micrometer readings do not represent the true sep aration of the surfaces because of thermal contraction due to different average temperatures of the steel before and after separation. The micrometer heads used in the apparatus are Brown and Sharpe instruments graduated in ten-thousandths (model number 293RS) furnished with ratchet stops. The micrometers are locked into 3/8 inch I. D. collars with set screws and attached to the plate by mounting each collar with three No. 2 screws through the support plate. The spindles touch stainless steel anvils 1/2 inch in diameter on surfaces ground flat. These anvils are attached to a ring which moves freely but is closely fitted to the outside diameter of the hot water jacket. The ring is supported by three steel columns as shown in Figure 2. The leveling screws, which are 5/16-24 case hardened machine screws moving in one inch thick mild steel threaded runs, rest on the same steel ring. The relative positions of the ring, the water jacket, and the support columns are maintained by corres pondence of punch marks and reference lines. By this means, 54 the bars are maintained parallel and in registration. The support columns were fabricated from one by two inch steel bar stock to make a stable platform which would provide max imum dampening of random vibrations. Construction of the water jackets.— Design of the water jackets was not dependent on hydraulic considerations because the high flow rates of circulating water assured good turbulence and very little temperature change in the circulating water. The jacket intervals were merely short pipe stubs to direct the incoming water to the center of the steel bars. The lower water jacket was made massive to stabilize the apparatus against vibrations transmitted through the building. An 8 inch 0. D. by 6 1/2 inch I. D. ring three inches high was welded to a six inch 150 pound rating A. S. A. blind flange to form the heavy base. This assembly was machined to provide a support for the bottom bar with mini mum obstruction to the linear conduction of heat through the cylindrical bar, as shown in Figure 2. The joint be tween the jacket and the bottom bar was made with a 0.010 inch thick polyvinyl plastic ring coated with resin sealer. The jacket assembly was chrome plated for corrosion resist 55 ance. Three leveling screws with lock nuts were threaded into the bottom of the jacket for use in leveling the therm al conductivity cell. The hot water jacket was machined for threaded attachment to the top bar using lathe cut threads in a 1/4 inch internal wall cutback on the bottom end of the jacket. The total height of the hot water jacket is three inches in order to provide space for suitable thermal insulation around the bar. The threaded section is 1/4 inch in depth using a thread count of forty per inch. The threaded joint between the jacket and the upper bar was made water-tight with resin sealer. The purpose of this design is to mini mize disturbances to linear temperature gradients in the top bar due to incomplete exposure to the constant tempera ture heat source. The effect of this disturbance is more critical on the thin section of the upper bar. With this design, about 95 per cent of the upper bar heat transfer surface in the jacket is contacted by the circulating water. Thermal guarding of the heat conducting bars.— Thermal guarding is supplied by two heating tapes wrapped around a thickness of 1 1/2 inches of urethane foam insula tion. Another one inch thickness of polystyrene foam 56 insulation covers the heating tapes. The heating tape out puts are independently controlled by variable voltage trans formers (Superior Electric Type 10B) to maintain the insula tion slightly warmer than the lower bar. EMF's measured from thermocouples inserted in the insulation one inch from the sides of the lower steel bar serve to indicate the ef fectiveness of the thermal guarding. The Constant Temperature Hydraulic Systems Two parallel constant temperature hydraulic systems were constructed to supply sufficient flows of hot and cold water to maintain the boundaries of the steel heat conduct ing bars at precisely controlled temperatures. The criterion for design of this apparatus was main tenance of a control range of plus or minus 0.005°F. Judg ing from thermocouple data at steady-state operation of the system, this objective is consistently achieved. The author received appreciated assistance from Mr. Fred Hutzell of the American Instrument Company (Aminco), Silver Spring, Maryland, in formulating the design of this system. The essential parts of the system are fifty gallon galvanized steel tanks with mixers for water surge, circu lating pumps, mercury thermoregulators, and controlled input 57 heating elements actuated by sensitive relays responding to the thermoregulators. The entire system, including the thermal conductivity cell, is installed in an air-condi tioned laboratory protected from exposure to direct sun light. The surge tanks, fabricated from 28 gauge galvan ized steel, are 24 inches in diameter by 28 inches high. Internal 3/4 inch piping on the inlet nozzles take suction from the center of the tanks about twelve inches from the water surface in the region where the mercury bulb of the thermoregulator is placed in order to maintain constant circulation of output water around the bulb. The return water is discharged through internal piping directed down ward over the heating elements. A two propeller mixer (Aminco catalogue number 4-660) with 24 inch shaft is mounted on the wooden top of each tank six inches from the rim. The contents of the tanks can be seen to be in rapid turbulent motion during operation of the unit. The heating elements are bent in about twenty inch diameter circular shapes over the bottom of the tank. A perforated shelf having about 50 per cent open area is mounted above the heating elements into which the bottom propeller of the mixer projects. Two 750 watt elements four feet in length 58 (Aminco catalogue number 34051) are provided for the hot water tank, and one 250 watt element four feet long (Aminco catalogue number 33951) for the cold water tank. Regulation of temperatures in the tanks is main tained with Precision Scientific Company Microset Differen tial Range Thermoregulators (mercury bulb type) mounted at the center of the tank. These were protected from undue vibration by foam rubber wrapping. Output from the thermo regulators is transmitted to Aminco Ultra-sensitive Mercury Regulators (Aminco catalogue number 4-204). For heating of the hot water tank, two circuits are provided. One heater operates continuously for coarse heating. The other is op erated by the relay responding to the thermoregulator. Power supply for each hot water tank heater is regulated by variable transformers of 1.0 KVA capacity (Superior Electric Autotransformers type 116U). The capacity of the single heater in the cold water tank is adjusted with a 0.45 KVA variable transformer (Superior Electric type 20 Autotrans former ) . Water circulation from each tank is provided by Eastern D-ll centrifugal pumps with buna-S rotary seals. The water pipes between the apparatus and the tanks are 1/2 inch schedule 20 or schedule 40 rigid PVC plastic which are 59 enclosed in wooden boxes for protection. Connections to the apparatus from the plastic pipes are made through brass couplings and unions to lengths of 1/2 inch flexible rubber hose. Circulation rates from the pumps under these condi tions are from eight to twelve gallons per minute. Thermometric Apparatus Thermocouple EMF measurements are made with a Leeds and Northrup K-3 potentiometer (catalogue 7553) in conjunc tion with a Leeds and Northrup DC electronic null detector (catalogue 9834). Current supply to the potentiometer is furnished by a special low current draw lead-acid storage battery (Leeds and Northrup catalogue number 7597). Other accessories include a certified standard cell and guarded cable for connecting the galvanometer to the potentiometer. The measuring dial of the K-3 potentiometer has a minimum calibration of 0.5 microvolts, and can be read by interpolation to 0.1 microvolt. The manufacturer states the limit of error is 0.5 microvolt in the low range, cor responding to an accuracy limitation of 0.02°F. using cop- per-constantan thermocouples. However, the results from repeated analyses of thermocouple data tabulated in Appendix D suggest attainment of 0.2 microvolt internal consistency 60 or reproducibility of data. This precision, better than 0.01°F., corresponds to the expected range of controllabil ity of the constant temperature sources. I In order to achieve the highest precision possible with this thermometric system, all reasonable precautions were taken. Recommendations outlined in the Leeds and Northrup K-3 Instruction Manual were followed for electrical guarding against stray currents. Thermal EMF's due to switching were minimized through use of Leeds and Northrup Type 31-3 brush type silver-silver alloy contact rotary selector switches. These were housed in an insulated box which also contained the terminal boards. The metal ele ments of the terminals were composed exclusively of brass screws and nuts. The potentiometer case itself was not grounded, but stable readings were obtained with the two bars of the heat flow apparatus short circuited and connect ed to ground. Both grounds on the DC null detector were connected, as well as the insulated portions of the guarded circuit at the storage battery and standard cell. Individual cold junctions were provided from each switch point of the 30 available. The cold junction leads were made from the same wire used for the hot junctions. 61 The cold junctions were fixed in plastic rings with epoxy cement and immersed in a one-pint capacity thermos bottle. / APPENDIX B THE EXPERIMENTAL PROCEDURE APPENDIX B THE EXPERIMENTAL PROCEDURE Measurement Technique Single liquid film.— Sufficient liquid is placed in the sample container to cover the surface of the lower bar with a film about 0.01 inch thick. The upper bar, elevated during sample addition, is lowered into the film while tilt ed slightly to displace air. When bubbles are no longer visible by sighting through the liquid between the separated bars, the upper bar is lowered to a free standing position centered on the lower bar. After rotating the movable ring and upper bar assembly to line up reference marks in the prescribed positions, the zero readings of the micrometers are made. This is done by carefully turning down the micro meter spindles until they barely contact the stainless steel anvils. When all three micrometers are adjusted to the po sition of minimum contact, each micrometer is tightened by two clicks of the ratchet stop. The force of each spindle on the anvil after tightening is about two ounces. This 63 64 procedure insures against forcing the ring into a bias as a result of the clearance provided between the ring and the jacket. After setting the ring by this procedure, the mi crometer spindles are backed away slightly and insulation is placed on the cell to permit thermal expansion to equalize around the apparatus. The time factor for equalization is about five minutes, after which the micrometer spindles are again brought down to touch. The micrometers are again tightened and the micrometer readings are recorded. The lifting, adjustment, and reading procedure is repeated until three successive readings in the zero position agree within 0.0003 inch for each micrometer. The average value of the three zero readings is taken as the basis for establishing the upper bar parallel above the lower bar when the upper bar is elevated on the leveling screws. The upper bar assembly is lifted from the bottom bar by turning the leveling screws, first taking care that the micrometer spindles are backed off the anvils to avoid for cing the spindle screws and possibly moving the micrometer barrels in the set collars. The position of the upper bar is adjusted with the leveling screws to obtain a desired sample thickness by testing for a constant difference in micrometer readings from the zero position. Care is taken 65 that bar and ring alignments on the reference marks are maintained, since torque from the screws acting on the screw anvils is sufficient to displace the upper bar assem bly. Additional liquid is added as required to keep the upper bar surface submerged. In order to observe the liquid level in the sample container, part of the insulation is removed. Final equilibrium readings are taken after waiting for an interval of time with the insulation in place. The two bars are accurately made parallel by this procedure, but their distance apart is not equal to the difference in micrometer readings due to contraction of the metal as a result of decreased average bar temperatures after separation. The metal bars reduce in length as much as 0.0020 inch between equilibrium bottomed and elevated positions. Optical measurement of the actual surface sep aration was made using a micrometer slide cathetometer, Gaertner catalogue number M940-301A, with a Gaertner micro scope, catalogue number M-101A, and M-220 objective mounted in the slide. The cathetometer is moved into position at the apparatus and leveled using screws on the tripod base for making each measurement. The object lens is approxi mately one inch from the outer surface of the glass ring when the cathetometer is in position. The edges of the 66 upper and lower bars are located in the cross hairs of the microscope viewing through the glass containing ring. The glass ring, made of pyrex, has a refractive index close to that of many fluids. However, surface irregularities of the glass both inside and out give rise to optical aberra tions which are possibly of significance in the measurement of thickness. The glass thickness is about 0.1 inch on the average, and the distance between the inner surface of the glass and the edge of the bar is also approximately 0.1 inch. Systematic error due to this source is reduced using readings of the cathetometer from three random positions for each optical measurement. At each position, three measure ments are made at each surface, with a total of eighteen readings recorded for a set of optical measurements. Single liquid measurements for mercury were carried out using the micrometer differences only. The accuracy of thickness measurement is satisfactory for mercury because the average bar temperatures change very little due to the low thermal resistance of mercury. Double liquid films.— When double liquid films are to be measured, an additional requirement is that the sur face of the lower bar must be accurately leveled with 67 respect to the horizontal. If horizontal levelness were not obtained, a short circuit heat path would exist in the sam ple where the better conducting fluid was thicker. The surface levelness is adjusted with three 5/8 stainless steel bolts threaded into the cold water jacket standing on the cell support. A precision tubular level instrument (Gaert- ner catalogue number M-482) is used to check the surface levelness. One scale division of the level instrument equals a ten second angle which represents a deviation of 0.0003 inches from the horizontal over the diameter of the bar. In making the level test the lapped surface of the Gaertner tubular level instrument is pressed onto the lower bar surface. The test for levelness is very sensitive to the degree of cleanliness of the two surfaces in contact. Small pieces of lint and other foreign material which are barely visible change the level reading significantly. In order to be sure the level indication is unchanged by ran dom surface imperfections or foreign material, the level instrument is switched end to end on a given diameter until the indicator bubble comes to rest in the same place, within allowable tolerances, relative to one end of the level. The best attainable agreement between bubble rest points in end to end switches was one-half scale division, which sets the 68 tolerance at a net deviation from horizontal of about 0.00015 inches over the diameter of the bar. Optical measurement of double liquid films also re quires location and measurement to the liquid-liquid inter face. The interface appears clearly and reproducibly when two transparent fluids are in the sample space. However, when mercury is one of the fluids the upward curving mercury meniscus requires focusing of the microscope into an appre ciable depth of fluid in order to locate the meniscus. The longer optical distance through liquids is suspected of giving rise to significant diffraction errors in the optical measurement. Accurate determination of fluid thicknesses for tests using mercury as one of the liquids requires a variant in the described technique for sample thickness measurement. The zero reading is determined without fluid addition. Mercury is then added to form a stable layer on the leveled surface of the bottom bar. A stable layer of mercury is about 0.13 inches thick. The upper bar is raised and leveled to provide an air gap of about 0.07 inches. The mercury surface can be observed clearly and reproducibly through air, but the distance from the surface to the lower bar cannot be measured directly. A reference mark and cross index has been cut into the glass ring with an alundum 69 crystal. This mark has been calibrated with the catheto- meter to determine its dimensional relationship to the top and bottom surfaces. The mercury thickness is obtained by difference through measurement of the distance from the mer cury surface to the reference mark. After clear liquid is added over the mercury to fill the sample space and the cell attains thermal equilibrium, the total sample thickness is found by measuring the distance from the top bar surface to the reference mark. Experimental difficulties were encountered with pre paration of double liquid films with liquid layer thickness es a few thousandths of an inch spread over the thirty square inch area of the steel surface. Surface forces in the presence of competitive or selective wetting activity tend to bring about contraction in surface areas of the films. The natural tendency for a free fluid is to form a minimum surface which is a spherical shape. This tendency made it impossible to employ liquids except those of high enough viscosity to form stable layers that resisted the tendency to contract. Great care had to be exercised when placing the top layer of fluid over a thin film of liquid on the lower surface to avoid breaking the film and allow ing the fluid on top to wet the lower steel surface. A 70 minimum thickness of the lower fluid was found to be neces sary to maintain stability of the two layers. Thermal gradient measurements.— Thermal gradient measurements for computing thermal resistances have been made for at least five film thicknesses for each sample ex amined, although a fewer number of data values are reported for some data sets in the Appendix D summaries when a data point has been removed because of known error. After deter mining the zero micrometer readings, the upper bar setting is adjusted to obtain sample thicknesses over the required range to complete the analysis, adding or removing fluid as necessary. Approximately one hour is required to reach temperature equilibrium after each sample thickness adjust ment. Thermocouple EMF readings, made after calibrating the potentiometer current to the standard cell, are repeated in fifteen to thirty minute intervals to check for reproduc ibility after equilibrium is assumed. An average deviation of 0.2 microvolt from the previous readings at each level is considered the maximum allowable deviation to conclude a set of readings at a given sample thickness. When unstable thermocouple readings occurred, they could be traced to one of the following causes: (1) mechanical breakdown of some 71 component of the constant temperature water supply system? (2) poor circuit connections at the thermocouple switching terminal boards; (3) broken thermocouple cold junctions; (4) detached ground from the cell or galvanometer. There was no evidence that thermocouple junctions in the bars were subject to serious instability or drift, because all inci dence of such instability disappeared when one of the men- . tioned sources of trouble was located and corrected. During several tests, a thermocouple became unstable due to occur rence of a source of difficulty. Thermocouple readings were omitted from analysis under this circumstance, which ac counts for occasional absence of data in the Appendix D summaries. Source and preparation of liquid samples.— Mercury was obtained originally from a supply which had been chemi cally treated and distilled and was reused throughout the reported series of runs. There was no reaction or attack on the plated surface on the lower bar judging from lack of damage to the surface evidenced through visual inspection. The mercury came into contact with pyrex glass, cured epoxy resin, and toluene or water in addition to the plated steel. It can be assumed that the mercury remained in a state of 72 high purity, inasmuch as no dirt skin reappeared on the mer cury surface after it had been cleaned and allowed to stand for prolonged periods in a pyrex beaker (25). Nujol used in the investigation was taken from three one-pint bottles of extra-heavy grade which were purchased on separate occasions. Single fluid thermal conductivities obtained for each of these bottles can be assumed identical through statistical inference. According to information registered with the Food and Drug Administration by the pharmaceutical firm marketing this product, Nujol is purely a paraffinic hydrocarbon and contains no additives. Distilled water employed in the heat conduction ex periments contained 50 p.p.m. Triton-X wetting agent and 100 p.p.m. sodium dichromate inhibitor. Tests on distilled water with the addition of Triton-X and with both Triton-X and sodium dichromate were not statistically different from tests on pure distilled water. Toluene and glycerol utilized in the tests were A. C. S. analytical reagent grade. However, this quality only specifies approximately 95 per cent purity. About 50 p.p.m. Triton-X was added to the glycerol to aid wetting of the steel surface. In addition, a few parts per million of ferroin dye was added to the glycerol for improved identification of the glycerol-toluene interface. APPENDIX C ANALYSIS OP THE DATA APPENDIX C ANALYSIS OF THE DATA Calculation of Resistance The average EMF at each thermocouple layer is calcu lated. EMF gradients, which are proportional to heat flux through the bar, are evaluated in the lower bar from aver age EMF's for the 3-4 and 3-5 levels. Correction to thermo couple EMF readings and precision of EMF measurements are estimated by calculating regression coefficients and re gression constants for each thermocouple assuming a linear relationship between the difference of thermocouple EMF reading and average EMF for the bar as the dependent varia ble. The linearity of this regression is assumed by reason ing that the difference between EMF of a thermocouple and the average EMF of the bar is proportional to the linear gradient. When the temperature gradient in the bar is zero, there is no heat flow and all EMF's should be identical. Calibration corrections to EMF readings are made by deter mining the residual EMF by extrapolating to the regression 75 76 constant at zero gradient. The precision of individual thermocouple EMF measurement in relation to average EMF of the bar is estimated by the regression variance. The re sults of EMF gradient analysis for each data set is given in the "B" tables of Appendix D. Equivalent resistances are calculated for the liquid between the surface of the bars from differences in correct ed average EMF data between thermocouple levels in the upper and lower bars divided by the EMF gradient in the lower bar. Since the gradient is expressed as rate of EMF change per inch of steel, the calculated resistance has units inches of steel. The calculated resistance values include the resistance of steel in the bars between the thermocouples and the steel surfaces as well as any steel-liquid inter facial resistance. Regression coefficients, regression constants, and variance of the resistance vs. film thickness regression are evaluated assuming linearity between film resistance and film thickness data. The assumption of proportionality between resistance values and liquid film thickness is rea sonable if the possibility of appreciable heat leaks or losses proportional to average temperatures of the upper and lower bars can be disregarded. The result of error 77 the regression coefficient is proportional to an estimate of the reciprocal value of the liquid thermal conductivity, the regression constant represents an estimate of the steel thermal resistance between the thermocouples and steel- liquid interface. In addition, the regression constant will include the resistance of a liquid film between the steel surfaces caused by surface imperfections which trap some of the liquid in voids when the upper bar is free standing on the lower bar. The presence of any steel-liquid interfacial resistance would be included, although it would be masked by the indeterminable liquid film in voids between the sur faces. Replicate linear regression data obtained for each of the five fluids during the course of the experimental study were examined for homogeneity by analysis of covari ance after testing for equality of variances by Bartlett's test. In all cases, Bartlett's test and between groups tests for equivalence of the regression coefficients were within 95 per cent statistical limits. The result of this analysis permitted use of the combined data in pooled re gression coefficients and regression constants having the improved confidence limits given in Tables 2 and 3. 78 Estimation of Error Estimates of error are made using weighted average variances calculated for each thermocouple level from vari ances of the EMF gradient regression data. Variances com puted from weighted averages produced a conservative error estimate because of the large influence of individual devi ant variances. Pooled variances cannot be logically em ployed because there is no basis for assuming that each thermocouple variance is drawn from the same population. The standard deviation of a difference in level EMF's is calculated from the form The subscripts refer to thermocouple levels considered in the calculation. The calculation of standard deviation for a resistance value is carried out using the equation in which a and b refer to the thermocouple levels from which the gradient is derived. Thus the EMF difference (1) x 2 . R (2) /\ Eak represents the difference between levels a and b in 79 the lower bar. The subscripts c and d indicate the thermo couple levels on opposite sides of the liquid film used to compute the EMF difference A EC(j. Computation of the standard deviation of a regres sion coefficient is accomplished using the value for sR and the standard deviation of the optical thickness measurement s^. The thickness measurement standard deviation, s^, was estimated from analysis of scattering of optical measurement observations for a series of tests. A value for sL of 0.000032 inch was obtained assuming nine independent thick ness measurements for each sample thickness, L. The esti mate of regression coefficient standard deviation is made from the error estimates of R and L using the equation where B represents the regression coefficient. The estimate of regression standard deviation may be compared to the experimental value by computing the esti mate sreg//lT, where N is the number of pairs of R and L from which the experimental regression was based. 80 Evaluation of Residual Resistance The residual resistance due to the liquid-liquid interface in the path of heat flow through the apparatus is computed by difference by combining regression data on the two-liquid system and regression data for the single heavier liquid. Resistance measurements at several sample thick nesses are employed to reduce the variance for resistance estimates of the sample at the measured thickness of the heavier film. Regression of resistance data with thickness meas urements obtained from a single set of data for two liquid systems resulted in high variance estimates of the regres sion coefficient. This was the result of using the narrow band of lighter film thicknesses permissible for EMF dif ferences sufficiently high to avoid excessive gradient de termination error. In order to obtain an estimate for the resistance of the double film at the heavy film thickness, the double film data were treated by analysis of variance assuming the pooled regression coefficient and regression constant from single fluid analysis as true population para meters. The observed resistance, Rho' at the heavy film thickness, L^, was evaluated using the lighter film 81 regression coefficient, Be, to compute the mean regression constant, g, and its variance from each resistance, R, and thickness, L, of n observations in the two film data, where Be is the lighter liquid population regression coefficient from the pooled regression analysis. This estimate of the resistance of the heavy film is compared to an estimate made from the heavy film regression coefficient, Rhc, by the calculation in which is the regression constant population parameter. Comparison of the heavy film resistance estimates derived from two film data on one hand and single film re gressions on the other requires a statistical test for the significance between samples assumed to have the same mean but drawn from populations having different variances. The technique introduced by Aspin was employed for evaluating the significance of the residual resistance where the resid ual between means Rjj0 and R^c drawn from populations having (4) (5) (6) (7) 82 2 2 variance estimates s£ and s2 is tested for significance by the t statistic at the OC significance level. &Ac. — residual 1 ^,c/yj'4'* + ^ where f is the degrees of freedom determined from The values of f^ and f2 are one less than the degrees of freedom for the estimate of the regression variance, s£, and the estimate of the mean regression constant variance from the two film data, s|, respectively. The three replicates of the test for residuals at a liquid-liquid interface may be combined for improving con fidence limits of an averaged residual. A pooled variance is utilized for establishing these confidence limits with one less degree of freedom than each of f values in equation (9), provided it can be shown that the variances are homo geneous. The t statistic is used with the same degrees of freedom to evaluate the pooled confidence limits. It can then be determined whether significant differences exist between the residuals computed from independent measure ments. The same treatment is applied to tests between sam ple sets for each independent mode of observation. 83 Example of Calculation Mercury-water data will be used to demonstrate the data reduction procedure. The Set 1 data for mercury-water (given in Tables 24A and 24B of Appendix D) and Set 2 of the water data (given in Tables 6A and 6B) will illustrate the calculations for two film and single liquid film data treat ment. From average EMF readings, given in microvolts at each thermocouple level, the first estimates of gradients are obtained using the measured distances of 3.502 inches between levels 3 and 5, and 1.742 between levels 3 and 4. For the second run in the Set 2 water data of Table 6A, the gradients are grad 3-5 = 1597.3 - 1214.3 = 109.4 microvolts/inch 3.502 grad 3-4 = 1597.3 - 1407.4 = 109.1 microvolts/inch 1.742 The first estimate of gradients are employed to evaluate zero EMF corrections given in the right column in the top portion of Table 6B by means of average EMF difference re gressions for each thermocouple. The regression standard deviation in Table 6B can be used to evaluate confidence limits of the zero correction. Zero corrections from thermocouple data analysis determined corrected gradients of 109.4 microvolts per inch for the 3-5 levels and 108.1 for the 3-4 levels in run 2 of Set 2 water data. In calcu lations for the mercury data, the confidence limits of the zero correction were too wide to be of value because the low thermal resistance of mercury did not permit accurate projection of the gradient data. The variance of gradient estimates is obtained by Equation (1) using the weighted average thermocouple stand ard deviation from the gradient regression. For the 3-5 gradient, the variance square root (standard deviation) is sgrad = y 0.422 + 0.102 = 0.43 The resistance of the film is determined by the EMF differ ence across the film divided by the gradient in the steel, which for resistance between levels 2 and 3 determined by the 3-5 gradient for run 2 of Table 6 is R = 2057t. i„z 1598|3 = 4.195 inches of steel 109.4 The standard deviation of the resistance is the square root of the variance computed from Equation (2) as follows: 85 sR = 4.195 ^ = 0.0067 inches of steel where the numerator of the first term under the radical is the standard deviation of the EMF difference between levels is obtained by computing the error from EMF variances and thickness measurement variance using Equation (3) for each run. Term by term substitution into Equation (3) produces the estimate of error in the regression coefficient, B, which for run 2 of the Set 2 water data is where the experimental regression coefficient value from Table 2 of 76.8 is employed for B. The quotient of the average value of sreg from the series of runs in Set 2 for 2-3 resistances and 3-5 gradients and the square root of the number of runs is computed and reported as an estimate of the regression standard deviation. The zero thicknesses are omitted in this calculation. As given under the head 2 and 3 computed in the same manner as Sgra(j using Equation (1). An estimate of error in the measurement technique } j f 0.0067 ^ 2 + ( 0.000032^ yj \4.195 ) \ 0.0412 ) = 0.137 86 ing Computed Standard Deviation in Table 6B, the estimate is 0.074. Note that sreg is dimensionless, having the same significance as the regression coefficient in Table 2. Regression results for replicate sets were tested for homogeneity by analysis of covariance, using the statis tical formula Pk-1, N-2k = (Bi ~ Ba>2sk<*j> x _______ N-2k (10) K ' 1 V # * BiSk(xi> using the notation k = number of data sets, or groups N = number of data runs B^= regression coefficient for set i Ba= pooled regression coefficient = **k(yj) Sk(xiYi> 0 2 The terms s^(xf), Sfc(y^)< and Sk^xiyi^ represent the sum of squares and cross products of the dependent and independent variables R and L respectively for each data pair, i, cor responding to a run for each of the sets, k. The combined data for the water sets for 2-3 EMF differences to determine resistances with 3-5 gradients gave S^x^) = 0.0314130 87 Sfcty?) « 187.388 S ^ x ^ ) = 2.42596 which for N of 22 and k of 4 resulted in Ba = 77.23 F3,14 = °’16 The low value of the F statistic indicates a high order of homogeneity among regression coefficients from the four data sets for water. Based on the variance of the pooled coefficient of 0.00172 with N-p-1, or 17, degrees of free dom, the 90 per cent confidence limits for the estimate of Ba is * 0.50. The pooled regression constant, Aa, is 1.02 with confidence limits of - 0.03. Pooling of the mercury data sets in the same manner resulted in the values 6.05 for B_ and 1.05 for A as reported in Tables 2 and 3 for a o 3-5 level gradients and 2-3 level EMF differences across the films. Although the data between sets for each liquid can be shown to be homogeneous, pooling of data in covariance treatment is permitted only if variances between groups are homogeneous. Bartlett's test was employed to test for equivalence between variances from the regression of data in each of the sets, using the statistic in which where and f are the degrees of freedom for each set and the pooled data respectively. The regression standard devi ations from Tables 5B through 8B were pooled to obtain the value of 0.00172 for the pooled variance. Substitution into Equation (11) using k of 4 and f^ two less degrees of free- of 3.15. This result indicates variances of the water data sets resulting from linear regression are homogeneous and grouped close to the population mean. Equations (4), (5), and (6) are utilized to compute the regression constant and its variance for each set of the two film data in order to determine resistances of the mer cury-water film at the thickness of the mercury film alone. For Set 1 of the mercury-water film data given in Tables 24A and B, individual values of the regression constant g are calculated from resistances determined from differences between levels 2 and 3 using 3-5 gradients. For example, a typical estimate of the regression constant g is dom than the number of runs for each set resulted in 89 g = 4.383 - (77.2)(0.1621) = -8.131 inches using the run 1 data in Table 24, and the population re gression coefficient for water as obtained by pooling the single film water data. The average, g, for Set 1 of the mercury-water data is -8.145, found by determining a value for g from the data of each run of the 2-3 EMF difference and 3-5 gradient results. The variance of these g values is found through Equation (5) to be 0.000625. By substitu tion of the average, g, into Equation (6) along with the observed mercury film thickness and population regression coefficient, the estimate for the observed resistance of the heavy film for the Set 1 data is Rho = (77.2)(0.1280) - 8.145 = 1.74 inches From Equation (7), the calculated value of the heavy film resistance is obtained by substitution of the mercury popu lation parameters Rhc = (6.05)(0.1280) + 1.05 = 1.82 inches The difference between these two quantities is the residual, -0.08, the significance of which is evaluated from the var iances of Rho and R^c estimates using Equations (8) and (9). Substituting values for variance and degrees of freedom 90 from the two film regression constant analysis and the pooled value of the mercury single film regression analysis into Equation (9), 1 = 1 (______ 0.00013______ ^ 2 + 1 { 0.000625______ V f 25 \0.000128 + 0.000625J 3 ^0.000128 + 0.000625^ = 1 4.3 Using the t statistic for 4.3 degrees of freedom, the 90 per cent confidence limits for the estimate of the residual are obtained, as indicated by Equation (8), residual = 0.08 - (2.10)(0.000128 + 0.000625)* = 0.08 - 0.06 inches of steel Simple means of mercury-water residual data for each sample are shown in Table 1 along with confidence lim its for the means calculated from pooled variances after testing for homogeneity of the variances between sets using Bartlett's test. A test for significance of residuals be tween independent observations (columns) is performed using the F statistic by comparing the variance between measure ments computed from the range of the data to the variance obtained by pooling the experimental results. In the four samples with three degrees of freedom, the F321 statistic 91 has a value of 8.66 at the 95 per cent level. The range of Set 1 residuals determines a variance of 0.0069, estimated from 0.486 of the range of 0.19 for observations reported in Table 1. Variances of independent measurements, in addi tion to the value of 0.00075 for the 2-3 EMF difference and 3-5 gradient (the quantity in the brackets above), were as follows: 0.00160 for resistance measurements between levels 1 and 4 using the 3-5 gradient, 0.00060 for levels 2 and 3 with the 3-4 gradient, and 0.00089 for 1-4 difference and 3-4 gradient. A total of 21 degrees of freedom resulted from individual degrees of freedom of 3.5 (as shown above), 3.3, 10.2, and 8.0 for each respective measurement. From these data, a pooled variance of 0.00082 was determined. The ratio of the estimate from the range and the pooled value is 8.4. Therefore the analysis indicates that the independent measurements are drawn from a population con taining 95 per cent of measurements of the sample treated in Set 1. Similar treatment of the row data (between sets) shows greater homogeneity inasmuch as the range of data in the given analysis is the greatest among the mercury-water results. APPENDIX D TABULATION OF EXPERIMENTAL DATA APPENDIX D TABULATION OF EXPERIMENTAL DATA Single film data are given in Tables 5 through 23. Tables 24 through 35 contain data for double film sets. Thermocouple EMF's as recorded and average total film thicknesses are tabulated in the "A" parts. The "B" tables are in three sections: (1) the top portion gives the re sults of thermocouple data analysis; (2) the center portion contains corrected gradient calculations, resistances com puted from the 3-5 level gradients, standard deviations of the 2-3 resistances for this gradient, and standard devia tion of regression coefficients derived from the 2-3 resist ance; (3) the bottom portion of the table lists observed standard deviations for the linear regression on resist ances using 3-5 level gradients, and the computed regression standard deviation for 2-3 resistances as determined from error estimates. The units for values in the "B" tables are as fol lows: (1) the EMF standard deviation, weighted average 93 94 standard deviation, and zero gradient correction units are microvolts. The regression coefficient units are inches of steel. (2) the units of EMF gradients are microvolts per inch of steel; the units of resistance are inches of steel; the units of resistance standard deviation are inches of steel; and the units of coefficient standard deviation are the ratio of liquid resistance per unit of length to the steel resistance per unit of length, dimensionless (see Table 2 units). (3) the regression standard deviations are similarly the dimensionless ratio of the liquid resist ance per unit of length to steel resistance per unit of length. TABLE 5A EXPERIMENTAL MEASUREMENTS FLUID - WATER SET 1 THERMOCOUPLE DATA LEVEL EMF, MICROVOLTS RUN 1 2 3 4 5 6 NO. 3 1 1887.0 1823.3 1768.5 1704.3 1644.4 1599.9 2 1892.5 1826.3 1775*4 1704.5 1644.8 1598.5 3 1894.9 1829.0 1777-6 1705.0 1647.6 1601.0 4 1899.3 1833.0 1783*3 1707-4 1651.2 1604.0 5 1897*6 1832.2 1787.0 1707.2 1653*4 1605.6 5 6 1466.0 1445.2 1428.4 1405.0 1386.9 1372.4 7 1454.2 1434.0 1420.6 1397*1 1379*3 1365*8 9 1457*4 1437*3 1421.8 1399.0 1381.5 1367.3 10 1468.6 1447.8 1432.1 1407.0 1388.1 1373*6 4 11 1677*5 1636.0 1607.1 1555*5 1517*9 1488.3 13 1679.0 1636.1 1603.6 1556.1 1518.2 1488.1 14 1680.9 1638.5 1605.1 1556.6 1520.0 1490.0 15 1681.8 1639*8 1606.5 1557*9 1521.3 1491.4 1 16 2067.4 2077.6 2090.4 2107.5 2115*4 2121.7 17 2076.2 2086.5 2097-5 2115*3 2122.1 2128.6 19 2071.0 2082.0 2091*0 2112.7 2119*1 2126.9 20 2059.1 2070.0 2077*0 2103*2 2109*2 2118.3 2 21 2030.7 2045.6 2060.3 2081.3 2092.3 2103.1 23 2020.4 2036.5 2051.4 2075*9 2087.8 2099.2 24 2016.4 2032.0 2045.6 2071.5 2083*0 2095*0 FILM THICKNESS (INCHES) 0. 0.0115 0.0207 0.0419 0.0610 0.0828 TABLE SB ANALYSIS OF EXPERIMENTAL DATA FLUID - WATER SET 1 THERMOCOUPLE EMF VS, GRADIENT ANALYSIS 96 LEVEL THERMO EMF WGT• AVG. REGRESSION ZERO COUPLE STANDARD STANDARD COEFF. GRADIENT DEVIATION DEVIATION CORRECTION 3 1 2.806 0.954 1.657 2.9 2 0.985 1.780 -6.2 3 0.478 1.783 -4.3 4 0.794 1.813 -3.3 5 2.560 1.761 2.4 5 6 0.604 0.232 -1.713 -1.2 7 0.450 -1.803 -1.6 9 0.391 -1.776 -1.9 10 0.174 -1.681 -2.0 4 11 1.734 0.592 -0.023 3.2 13 0.313 -0.016 2.2 14 0.499 -0.008 3.2 15 0.477 -0.014 5.0 1 16 1.155 0.740 0.200 -2.3 17 0.632 0.237 1.9 19 0.698 0.173 4.0 20 2.156 0.104 -0.5 2 21 0.998 0.425 -0.097 -2.2 23 0.320 -0.220 2.3 24 0.447 -0.219 -2.4 EQUIVALENT RESISTANCE - COMPUTATION AND ERROR ANALYSIS EMF EQUIVALENT STANDARD DEVIATION GRADIENT RESISTANCE RESIST COEFFI ANCE CIENT LEVEL 3-4 3-5 2-3 1-4 DIFF. RUN 1 121.1 123.6 1.030 3.167 2.136 0.0088 0. 2 108.8 110.7 1.882 4.011 2.129 0.0106 0.4866 3 99.3 100.7 2.712 4.827 2.114 0.0128 0.3867 4 84.9 86.7 4.263 6.410 2.147 0.0183 0.3392 5 74.0 75.5 5.809 7.946 2.137 0,0257 0.3458 6 65.1 66.3 7.492 9.615 2.124 0.0354 0.3690 REGRESSION COEFFICIENT LEVEL ■ 2-3 LEVEL 1-■4 OBSERVED STANDARD DEVIATION 0,01(6 COMPUTED STANDARD DEVIATION 0 ,1 7 4 0.038 TABLE 6A EXPERIMENTAL MEASUREMENTS FLUID - WATER SET THERMOCOUPLE DATA LEVEL EMF, MICROVOLTS RUN 1 2 3 4 5 NO. 3 1 1834.9 1594.9 1470.6 1 395*4 1346*4 2 1 845*0 1 597*6 1 471*3 1 394*9 1 340*5 3 1 844.0 1 595*4 1489*2 1 393*0 1 338*9 4 1 849*6 1 598.3 1 471*5 1 394*9 1 340*5 5 1 849*1 1600*5 1 474*2 1 397*7 1 343*3 5 6 1288.6 1216*6 1179*4 1157*6 1140*1 7 1278.7 1209*6 1174.1 1153*5 1136*9 8 1278.3 1209*6 1174*1 1153*5 1136.9 9 1295.5 1221.4 1183.5 1161.0 1143*2 4 11 1561*4 1406.0 1325*3 1277*8 1241.8 12 1 566*6 1 408.1 1327*1 1278.1 1242.4 13 1565*7 1407.0 1326.4 1277*4 1241.7 14 1566*9 1408.0 1327*0 1278.0 1242.0 1 16 2067*0 2101*7 2121*1 2133*0 2140*5 17 2073.0 2108*5 2127*1 2137*9 2144.6 18 2077*9 2111*5 2129*7 2140.0 2144.6 19 2057*3 2095*1 2116.0 2128.0 2135*9 2 21 2013*9 2065*8 2093*6 2109*9 2120*5 22 2008*9 2066.5 2097*1 2114.5 2125*6 23 1998.6 2055*7 2086*6 2104*7 2116*5 24 1981.1 2039*5 2072.0 2091*5 2104.4 FILM THICKNESS (INCHES) 0. 0.0412 0.0814 0.1217 0.1616 TABLE 6B ANALYSIS OF EXPERIMENTAL DATA FLUID - WATER SET 2 THERMOCOUPLE EMF VS. GRADIENT ANALYSIS LEVEL THERMO EMF WGT. AVG. REGRESSION ZERO COUPLE STANDARD STANDARD COEFF. GRADIENT DEVIATION DEVIATION CORRECTION 3 1 1.462 0.417 1.633 9.3 2 0.361 1.770 -2.5 3 0.281 1.777 -4.9 4 0.600 1.816 -5.8 5 0.280 1.783 -0.6 5 6 0.071 0.098 -1.722 -1.4 7 0.263 -1.787 - 1.1 8 0.195 -1.791 -0 .8 9 0.128 -1.685 -0.5 4 11 0.615 0.209 -0.045 4.0 12 0.237 o.ooi 1.5 13 0.260 -0.001 1.0 14 0.298 0.007 0.9 1 16 0.536 0.346 0.207 -1.1 17 0.446 0.224 2.8 18 0.982 0.264 1.5 19 0.173 0.156 -2.4 2 21 0.107 0.321 -0.119 -1.8 22 0.467 -0.221 9.7 23 0.184 -0.230 0.6 24 0.893 -0.282 -9.2 EQUIVALENT RESISTANCE - COMPUTATION AND ERROR ANALYSIS EMF EQUIVALENT STANDARD DEVIATION GRADIENT RESISTANCE RESIST COEFFI ANCE CIENT LEVEL 3-4 3 - 5 2-3 1-4 DIFF. RUN 1 157.1* 159.7 0.973 3*164 2.191 0.0034 0. 2 1 08.1 109.4 4.195 6.387 2.192 0.0067 0.1366 3 82.9 83.8 7.339 9.527 2.188 0.0124 0.1333 4 67.4 68.2 10.402 12.592 2.190 0.0202 0.1504 5 56.8 57.9 13.377 15.572 2.195 0.0298 0.1712 REGRESSION COEFFICIENT LEVEL 2-3 LEVEL 1-4 OBSERVED STANDARD DEVIATION 0.060 O.O58 COMPUTED STANDARD DEVIATION O.O74 TABLE 7A EXPERIMENTAL MEASUREMENTS FLUID - WATER SET 3 THERMOCOUPLE DATA LEVEL EMF, M ICROVOLTS RU N 1 2 3 A 5 6 NO. 3 1 1705.2 I6A6.5 1597.9 1572.7 1659.3 1629.3 2 1711.6 1650.6 1601.0 1575.1 1662.5 1631.5 3 1708.5 16A9.A 1599.1 1573.5 1 665.0 1631 .A A 1711.7 1651 .A 1601.0 1575.3 1665.6 1633.5 5 1713.8 1652.6 1602.2 1576.8 1667.9 1636.0 5 6 1A15.A 1396.0 1379.7 1371.2 1A00.5 1390.5 7 1A11.1 1392.0 1 376.5 1 368.7 1 39A.7 1385.0 9 1A10.5 1 391.6 1 376.0 1 367.8 1 395.5 1 385.8 10 1A19.1 1398.7 1382. A 1373.6 1A03.0 1392.6 A 11 1562.5 1523.0 1A90.A 1A7A.2 1533.5 1512.9 13 156A.9 152A.3 1A91.5 1A75.A 1532. A 1511.7 15 156A.A 152A.9 1A91.8 1A75.5 153A.1 1513. A 1 16 1832.5 18A1.5 18A1.9 18A6.0 18A U 1 I8A5.9 17 1838.1 18A7.0 18A6.7 1 850.3 18A6.0 1 850.5 20 1 828.2 1 836.8 1 837.7 1 8A1.9 1835. A 18A0.5 2 21 1805.6 1 818.2 1 820.9 1 826.8 1 816.6 1 823.0 23 1799.6 181A.0 1818.1 182A.2 1811.6 1818.9 2A 1797.0 1 811.8 1 816.0 1 822.0 1 809.9 1 817.2 FILM THICKNESS (INCHES) 0 . 0.0156 0.030A 0.0A03 0.0110 0.0203 TABLE 7B ANALYSIS OF EXPERIMENTAL DATA FLUID - WATER SET 3 THERMOCOUPLE EMF VS. GRADIENT ANALYSIS 100 LEVEL THERMO EMF WGT. AVG. REGRESSION COUPLE STANDARD STANDARD COEFF. DEVIATION DEVIATION 3 1 0.311 0.338 1.634 2 1.170 1.768 3 0.411 1.748 4 0.261 1.800 5 0.642 1.830 5 6 0.435 0.261 -1.719 7 0*722 -1.803 9 0.143 -1.782 10 0.138 -1.679 4 11 0.892 0.439 -0.022 13 0.782 -0.002 15 0.271 -0.007 1 16 0.242 0.238 0.188 17 0.121 0.233 20 0.551 0.165 2 21 0.170 0.146 -0.100 23 0.133 -0.238 24 0.342 -0.248 EQUIVALENT RESISTANCE - COMPUTATION AND ERROR ZERO GRADIENT CORRECTION 4.2 -1.7 -1.5 -3.0 -3.3 -1.5 0.2 -1.4 - 1.6 2.3 1.5 2.5 - 0.1 1.6 -3.2 -2.7 2.9 1.5 EMF EQUIVALENT STANDARD DEVIATION GRADIENT RESISTANCE RESIST COEFFI ANCE CIENT LEVEL 3-4 3-5 2-3 1-4 DIFF. RUN 1 83.4 84.6 1.052 3.213 2.161 0.0046 0. 2 71.8 73.0 2.233 4.391 2.158 0.0063 0.2726 3 62.2 63.3 3.421 5.587 2.166 0.0088 0.2179 4 57.7 58.4 4.250 6.404 2.154 0.0110 0.2107 5 74.9 75.7 1.946 4.095 2.149 0.0058 0.3259 6 68.8 69.6 2.667 4.820 2.153 0.0071 0.2414 REGRESSION COEFFICIENT LEVEL 2-3 LEVEL 1--4 OBSERVED STANDARD DEVIATION 0 .0 3 4 COMPUTED STANDARD DEVIATION 0 .1 1 5 0 .0 2 9 TABLE 8A EXPERIMENTAL MEASUREMENTS FLU 10 - WATER SET THERMOCOUPLE DATA LEVEL EMF, MICROVOLTS RUN 1 2 3 If 5 N O * 3 1 1440.0 1490.6 1561.5 1665.1 1829.3 2 1444.3 1496.0 1568.1 1674.3 1845*0 3 1439.9 1491.2 1563.5 1670.1 1845*5 4 1442.9 1494.5 1567*6 1675.1 1855*5 5 1444.5 1496.1 1569.1 1676.5 1857*5 5 6 1 215.7 1 232.7 1 256.4 1291.1 1348.3 7 1211.1 1227.5 1250.1 1283.8 1338.5 9 1212.5 1229.3 1252.0 1285*5 1340.8 10 1218.0 1235.4 1259.6 1295*3 1353.9 4 11 1329.1 1362.5 1410.6 1479.5 1591.6 13 1330.5 1364.5 1412.5 1482.7 1598.5 14 1335.7 1370.0 1417*6 1486.6 1602.7 15 1330.1 1364.7 1412.5 1483.0 1599*4 1 16 2144.0 2133.0 2118.1 2096.0 2057*5 18 2138.9 2127.0 2110.5 2085*8 2045*5 19 2147*4 2136.6 2122.0 2099.3 2061.0 20 2131*0 2118.1 2099*6 2074.1 2033*4 2 21 2127*0 2112.3 2093.1 2064.1 2014.1 22 2117*4 2101.6 2079.7 2047.1 1992.9 23 2110.1 2093.6 2070.8 2037.2 1983.3 25 2099*4 2081.6 2057*9 2023*9 1969*9 FILM THICKNESS (INCHES) 0.1210 0.0913 0.0616 0.0314 0. TABLE 8B ANALYSIS OF EXPERIMENTAL DATA FLUID - WATER SET 4 THERMOCOUPLE EMF VS. GRADIENT ANALYSIS LEVEL THERMO EMF WGT• AVG. REGRESSION ZERO COUPLE STANDARD STANDARD COEFF. GRADIENT DEVIATION DEVIATION CORRECTION 3 1 1.849 0.620 1.566 10.1 2 1.035 1.711 4.4 3 0.292 1.773 -5.2 4 1.209 1.862 -8.6 5 1.416 1.866 -7.4 5 6 0.063 0.059 -1.726 -1.3 7 0.161 -1.792 -1.6 9 0.106 -1.784 -0.6 10 0.092 -1.684 -1.8 4 11 0.701 0.264 -0.060 4.0 13 0.118 0.009 0.4 14 0.512 -0.009 7.0 15 0.200 0.023 -0.7 1 16 0.590 0.335 0.266 0.2 18 0.173 0.175 0.8 19 0.643 0.265 3.8 20 0.847 0.122 -4.4 2 21 0.694 0.373 -0.070 4.9 22 °*222 -0.223 5.3 23 0.388 -0.253 -0.6 25 1.042 -0.283 -10.1 EQUIVALENT RES 1 STANCE - COMPUTATION AND ERROR ANALYSIS EMF EQUIVALENT STANDARD DEVIATION GRADIENT RESISTANCE RESIST COEFFI ANCE CIENT LEVEL 3-4 3-5 2-3 1-4 DIFF. RUN 1 64*2 65.1 10.290 12.465 2.175 0.0303 0.2265 2 74.0 74.9 8.038 10.218 2.181 0.0214 0.2060 3 87.9 88.9 5.714 7.892 2.177 0.0141 0.1926 4 108.0 109.5 3.377 5.559 2.182 0.0086 0.2102 5 141.3 143.1 0.994 3.171 2.177 0.0052 0. REGRESSION COEFFICIENT LEVEL 2-3 LEVEL 1-4 OBSERVED STANDARD DEVIATION 0 .0 2 2 0 .0 2 3 COMPUTED STANDARD DEVIATION 0 .1 0 5 TABLE 9A EXPERIMENTAL MEASUREMENTS FLUID - TOLUENE SET THERMOCOUPLE DATA LEVEL EMF, MICROVOlTS RUN 1 2 3 4 NO. 3 1 1740.5 1564.0 1490.0 1 1* 3.6 2 1744.9 1562.9 1488.5 1441.0 3 1747*5 1566.0 1490.4 1444.9 4 1748.3 1567*5 1491*5 1446.2 5 1742.0 1566.0 1490.8 1445.6 5 6 1416.2 1 359*0 1 335*0 1 320.4 7 1407 . 2 1 351*2 1 327*7 1 313.9 9 1409*0 1 355*2 1 332.0 1 317*6 10 1417*6 1 361.0 1 335*5 1 320.7 4 11 1577*3 1463*5 1 413*9 1 384.6 13 1580.8 1463.6 1413.4 1 382.4 15 1581*7 1464*6 1414.9 1385.0 1 16 1890.0 1918.5 1932.0 1938.5 17 1895*1 1923*7 1935*5 1941.6 19 1890.4 1922.5 1934.1 1940.7 20 1881.8 1915*8 1928.1 1935*8 2 21 1860.4 1903.6 1918.9 1928.7 23 1849.0 1897*0 1915*1 1925*8 24 1847*8 1893*1 1912.1 1922.9 FILM THICKNESS (INCHES) 0. 0.0125 0.0225 0.0319 TABLE 9B 104 ANALYSIS OF EXPERIMENTAL OATA FLUID - TOLUENE SET 1 THERMOCOUPLE EMF VS. GRADIENT ANALYSIS LEVEL THERMO EMF WGT. AVG. REGRESSION ZERO COUPLE STANDARD STANDARD COEFF. GRADIENT DEVIATION DEVIATION CORRECTION 3 1 0.513 0.286 1.694 1.0 2 0.837 1.812 -6.2 3 0.660 1.802 -2.7 4 0.562 1.795 -1.1 • 5 0.499 1.693 2.6 5 6 0.405 0.213 -1.718 -0.1 7 0.563 -1.758 -5.4 9 0.228 -1.796 0.3 10 0.361 -1.699 -0.1 4 11 0.536 0.274 -0.069 5.1 13 0.496 0.022 -0.1 15 0.121 -0.002 2.8 1 16 1.112 0.371 0.222 -2.4 17 0.346 0.256 -0.1 19 0.418 0.191 1.6 20 0.346 0.132 -1.4 2 21 0.686 0.331 -0.112 0.4 23 0.432 -0.259 2.9 24 0.546 -0.229 -1.6 EQUIVALENT RESISTANCE - COMPUTATION AND ERROR ANALYSIS EM F GRADIENT LEVEL 5-lf RUN 92.9 8.7 1 2 3 4 58.7 44.1 35.2 > 5 94.8 59.6 45.0 36.0 EQUIVALENT RESISTANCE 2-3 1-4 DIFF. 1.116 3.296 2.179 5.550 7.710 2.159 9.400 11.582 2.183 13.320 15.504 2.184 STANDARD RESIST ANCE DEVIATION COEFFI CIENT REGRESSION COEFFICIENT LEVEL 2-3 OBSERVED STANDARD DEVIATION 0.238 0.0048 0.0120 0.0235 0.0397 LEVEL 1-4 0 .2 4 6 0. 1.2736 1.0893 1.1928 COMPUTED STANDARD DEVIATION 0 .6 8 6 TABLE 10A EXPERIMENTAL MEASUREMENTS FLUID - TOLUENE SET 2 THERMOCOUPLE DATA LEVEL EMF, MICROVOLTS RUn 1 2 3 4 5 6 NO. 3 1 1876.7 1651.8 1560.2 1504*5 1530.5 1610.4 2 1888*2 1652.7 1558*5 1501*7 1528*6 1611.1 3 1852*3 1656*8 1561*7 1505*4 1532*0 1613*5 4 1896*7 1661*1 1564*7 1507*9 1534*5 1616*8 5 1893*5 1662.0 1565*6 1508.5 1535*1 1618*4 5 6 1465*5 1 389.6 1 359*6 1 341.2 1 350.3 1 375*9 7 1454*5 1382.7 1352*6 1335*0 1344.2 1368.6 9 1456.6 1 384.1 1355*0 1 337*5 1 345*2 1 370*9 10 1467*5 1 391*4 1 360*5 1 342.0 1 350*4 1 377*3 4 11 1673*1 1525*3 1463*8 1426*7 1444.4 1496*4 13 1676*4 1524.9 1462*6 1424*6 1442.4 1495*2 14 1677*8 1525*8 1463*8 1426*7 1444.6 1497*2 15 1679*6 1527*0 1464*9 1427*2 1445*3 1498.0 1 16 2077*9 2112*8 2129*9 2138*6 2135*5 2121.6 17 2083*5 2118*4 2134*7 2142.8 2140*6 2127*3 19 2077*5 2114*9 2132.0 2140*7 2138.6 2124*5 20 2066*7 2106.1 2124.0 2133*6 2130.8 2116.1 2 21 2040.0 2091*0 2112.6 2125*4 2121.0 2101*6 23 2025*2 2083*7 2108.3 2121.8 2117*4 2096.6 24 2021*8 2079*0 2104.1 2117*9 2113*5 2092.0 FILM THICKNESS (INCHES) 0. 0.0111 0.0211 0*0307 0.0260 0.0154 TABLE 10B 106 ANALYSIS OF EXPERIMENTAL DATA FLUID - TOLUENE SET 2 THERMOCOUPLE EMF VS. GRAD IENT ANALYSIS LEVEL THERMO EMF WGT• AVG. REGRESSION ZERO COUPLE STANDARD STANDARD COEFF. GRAOIENT DEVIATION DEVIATION CORRECTION 3 I 0.363 0.287 1.602 5.2 2 3 0.7 5if 0.61 i f 1.796 1.806 i f 0.366 1.833 -3.5 5 0.807 1.780 0.6 5 6 0.36h 0.173 - 1.712 - 1.0 7 0.3M+ -1.776 -3.9 9 0.381 -1.776 - 2.0 10 0.27if -1.691 -1.3 if 11 0.527 0.216 -O.O79 7.3 13 0.508 -0.006 1.5 lif 0.186 -0.015 3.8 15 0.268 0.001 3.7 1 16 0.5if5 0.183 0.230 -3.2 17 O.lifl 0 .2i f i f 1.0 19 0.217 0.190 1.6 20 0.165 0* 1 if 3 -3.6 2 21 0.1*16 0.227 -O.O99 -0 .6 23 0.if56 -0.256 if .2 2i f 0.165 -0.2if9 -O.if EQUIVALENT RESISTANCE - COMPUTATION AND ERROR ANALYSIS EM F EQUIVALENT STANDARD GRADIENT RESISTANCE RESIST ANCE LEVEL 3“i f 2-3 1 -if DIFF. RU N 1 119.1 122.3 1.115 3.309 2.19if 0.0031 2 75.if 5.508 7.686 2.178 O.O08if 3 57.2 58.6 9.268 11 .if 59 2.192 O.Oi 6i f k 46.2 if7.6 12.880 15*081 2.201 0.0271 5 51 .if 52.7 11.035 13.222 2.187 0.0213 6 66.7 6 8.8 6.973 9.172 2.199 0.0111 REGRESSION COEFFICIENT LEVEL 2-3 LEVEL 1 COEFFI CIENT 0. 1.2355 0.8835 0.8887 0.8655 0.9922 OBSERVED STANDARD DEVIATION O.O77 COMPUTED STANDARD DEVIATION O.ififO 0.072 '- '■ n ro — O ' VP z 1 “ o x ro N> K> ■ f v*» — ro — — © - j < r v n u » — O V O 'O O N c • p i —i I P X o > J N J M VO VO © v n ^ J oo ODOOOO M V u V u o « r 9 9 9 v n v n v n VP VP VP VOVO**J V P M 00VM A A A A z P I v n - J c c r v u vn ff'Vw • W W W vo oo vn — c • o 00 i p G O ODOOOO V w U i V n M O # • • • o ' o o - r 0 0 0 0 0 0 VP VP VP *3 VO VP • • • — KJ — v n v n v n M > J On • • • v o v n ^ J V m V m V m V m VP VC O V m • • * • v t i v o r o © • o Os - V w ^ 9 9 # oo op op V P O 'O ' N J O C r r r U i V m V w ro ro to V m U*V*V*> v n ^ ^ v n to OOODO A A A A V ' vn O -O -U . vn o vn v n r o w • • • > 1 © V P vo © ■ o ro iia N i v e i o • 9 A iii - o o r A A A £ £ £ V*»K>tO 9 9 9 V *V h Vh U i r v w u > r to O O V O - A A A A N J C f f ' o v e r • W W W O V C — to © • o K> Os ODOOOO VP VP VP ro u > v p A A A V m VO O ' A A A 0 0 0 0 -^ V u U iV w U t V m Vu I u U i VP to to V m 1 O © V O oo • A W <sJVO0D VCvwVC r c 9 V D o • © U ) ODOOOO VP VP VP O'ODVO 9 9 9 £S£ N iM V O 9 9 9 U >V>V> ?f¥ V w V w V w V m Vu to to ro O 9 9 f l 0 A A A A — ro — V m ODVP VD CP — © v p vc © U) O C O O O -*U> O^VCU) m x c p i oauiMvn — 2?g3£2? • • • • • OKINl © — cpvp v n v n v n o vo odVC oo • • • • • vo ro-e~u><r> f f f f f M - O — • • • • • **JVwVw O D © 8 8 ~v r~ m CDtt^OVi • • • • • v n v n v n v n v n C O V C N - • • • • • O -H ■n > r * ro c P i © X *T J 1 P I m 30 X Vm -n X « — 4 P i — 4 O ~ > X r “ 1 00 C > 1 “ o m P I 30 z ■ r o p i X c P I © > > I— IP — H c IP 30 P i vn X i p P I p i 21 — 4 H IP V m 107 TABLE 11B ANALYSIS OF EXPERIMENTAL DATA FLUID - TOLUENE SET 3 THERMOCOUPLE EMF VS* GRADIENT ANALYSIS 108 LEVEL THERMO EMF WGT. AVG. REGRESSION ZERO COUPLE STANDARD STANDARD COEFF. GRADIENT DEVIATION DEVIATION CORRECT 101 3 1 1.882 0.543 1.724 -0.4 2 0.337 1.836 -3.2 3 0.287 1.807 -3.8 4 0.A60 1.777 -1.9 5 0.743 1.656 4.0 5 6 0.190 0.101 -1.713 -1.6 7 0.245 -1.779 -0.8 9 0.174 -1.785 -1.0 10 0.184 -1.692 -0.7 4 11 0.417 0.200 -0.040 2.5 13 0.231 -0.002 1.5 15 0.336 -0.011 2.2 1 16 0.266 0.144 0.227 -1.9 17 0.142 0.246 0.8 20 0.286 0.154 -1.8 2 21 0.375 0.185 -0.093 -1.4 23 0.297 -0.264 3.1 24 0.269 -0.269 1.3 EQUIVALENT RESISTANCE - COMPUTATION AND ERROR ANALYSIS EM F EQUIVALENT STA N D A RD DEVIATION GRADIENT RESISTANCE RESIST COEFFI A N CE CIENT LEVEL 3-4 3-5 2-3 1-4 DIFF. RU N 1 82.0 83.9 1.112 3*311 2.200 0.0072 0. 2 52.3 53.0 5.391 7*572 2.181 0.0194 1.6893 3 45.0 45.9 7.210 9.399 2.189 0.0279 1.6184 4 39.3 40.0 9.165 11.362 2.197 0.0390 1.6860 5 35.1 35.9 10.929 13.124 2.195 0.0508 1.7988 6 31.6 32.4 12*784 14.998 2.214 0.0649 1.9388 REGRESSION COEFFICIENT LEVEL 2-3 LEVEL 1-■4 OBSERVED STANDARD DEVIATION 0.080 COMPUTED STANDARD DEVIATION O .783 0.087 TABLE 12A EXPERIMENTAL MEASUREMENTS FLUID - TOLUENE SET THERMOCOUPLE DATA LEVEL EMF, MICROVQuTS RUN 1 2 3 4 5 NO. 3 1 1310.5 1246*0 1426.5 1356.5 1273.6 2 1309.4 1245*7 1428.0 1356.9 1273.0 3 1307.1 1243.9 1425.8 1354.9 1271.3 4 1308.4 1245.0 1427.3 1356.2 1272.4 5 1310.6 1247.7 1429*0 1358.4 1274*7 5 6 1135.7 1114.6 1174.1 1152.6 1123.6 7 1132.7 1112.6 1169.8 1149.2 1121.1 9 1131.5 1111.2 1169.0 1148.2 1120.2 10 1136.3 1116.8 1177.8 1155.9 1126.4 4 11 1224.5 1182.0 1301.6 1256.1 1200.4 12 1224.3 1181.9 1302.1 1256.4 1200.0 14 1223.6 1181.5 1301.4 1255*5 1199*3 15 1222.6 1180.2 1301.3 1255*1 1198.8 1 16 2144.1 2154.7 2127*5 2138.5 2149*6 18 2148.0 2158.0 2131.7 2142.9 2153.3 19 2149.8 2159*3 2134.0 2144.6 2154.4 20 2140.5 2152.0 2122.3 2135.1 2146.5 2 21 2128.0 2142.3 2103.1 2119.5 2135*4 22 2127.1 2142.3 2100.5 21H.9 2135.0 24 2124.0 2139.5 2097*1 2114.6 2132.1 25 2113.7 2130.8 2085*5 2104.0 2122.7 FILM THICKNESS (INCHES) 0.0409 0.0613 0.0217 0.0315 0.0513 TABLE 12B 110 ANALYSIS OF EXPERIMENTAL DATA FLUID - TOLUENE SET if THERMOCOUPLE EMF VS. GRADIENT ANALYSIS LEVEL THERMO EMF WGT• AVG. REGRESSION ZERO COUPLE STANDARD STANDARD COEFF. GRADIENT DEVIATION DEVIATION CORRECTION 3 t 0.60if 0.17if 1.711 1.8 2 0.090 1.771 -1 .if 3 0.251 1.759 -2.8 i f 0.211 1.771 -2.1 5 0.286 1.747 1 .if 5 6 0.087 0.060 -1.732 -0.5 7 0.131 -1.795 -0.3 9 0.113 -1.783 -2.0 10 0.137 -1.692 0.3 i f 11 0.2if2 O.09if -0.022 2.8 12 0.150 0.001 1.6 lif 0.167 -0,007 1.3 15 0.161 0.022 -0.8 1 16 0.220 0.100 0.210 -0.6 18 0.136 0.236 1.9 19 0.12if 0.266 1.9 20 0.25if 0.1 i f 5 -0.9 2 21 0.127 0.076 -0.130 -0.1 22 0.127 -0.20if 2.7 2if 0.094 -0.222 0.5 25 0.207 -0.301 -5.5 EQUIVALENT RESISTANCE - COMPUTATION AND ERROR ANALYSIS EMF EQUIVALENT STANDARD DEVIATION GRADIENT RESISTANCE RESIST COEFFI ANCE CIENT LEVEL 3-if 3-5 2-3 1-if DIFF. RUN 1 if9.6 if9#9 16.321 18. if97 2.176 0.0177 0*if868 2 37.*f 37.7 23.718 25.901 2,183 0.0336 0.5500 3 72.2 72.7 9.203 11.386 2.183 0.0072 0.6079 i t 58.2 58.6 12.932 15.113 2.181 0.0121 0.5031 5 if 2.6 if 2.9 20.01if 22.199 2.185 0.0250 0.5088 REGRESSION COEFFICIENT LEVEL 2-3 LEVEL 1-if OBSERVED STANDARD DEVIATION 0.075 0.073 COMPUTED STANDARD DEVIATION 0.238 TABLE 13A EXPERIMENTAL MEASUREMENTS FLU 10 - MERCURY SET 1 THERMOCOUPLE DATA LEVEL RUN 1 NO. EMF, MICROVOLTS 2 3 A 5 6 3 1 1881.1 2 1883.6 3 1885.6 A 1885*0 5 189A.1 5 6 1A62.6 1A63.6 1A58.5 1A61.3 1A57.5 1AA8.5 7 1A58.6 1A58.8 1A55.5 1A5A.6 1A50.7 1AA1.3 8 1A5A.5 1A55.5 1A55.2 1A56.0 1A50.2 1AA1.1 10 1A6A.A 1A66.0 1A60.2 1A65.0 1A61.6 1A50.5 A 11 1678.6 1681.5 167A.3 1671.5 1662.A 16A8.0 1A 1678.1 1681.3 1673.8 1670.6 1662.0 16A7.8 15 1681.5 168A.0 1676.5 1672.8 166A.A 1650.3 1 16 207A.2 207A.A 2076.6 2080.8 2081.6 208A.0 17 208A.2 208A.8 2086.0 2088.7 2080.6 2083.0 18 2080.6 2082.3 2081.A 208A.0 2085.A 2087.5 20 2070.A 2073.6 2070.5 2073*5 207A.7 2076.6 2 21 2038.2 2038.5 20A1.5 20AA.5 20A7.1 2050.3 23 2028.8 2028.7 2031*3 2035*0 2038.1 20A1.6 2A 202A.1 202A.5 2025.6 2028.1 2032.6 2035.A FILM THICKNESS (INCHES) 0 .0151 0 .0 1 0 0 0 .0 2 8 8 0 .0 5 0 3 0 .0 8 0 0 0 .1 1 8 7 TABLE 13B ANALYSIS OF EXPERIMENTAL DATA FLU 10 - MERCURY SET t THERMOCOUPLE EMF VS. GRADIENT ANALYSIS 112 LEVEL THERMO- EMF COUPLE STANDARD DEVIATION i f 1 1 2 3 if 5 6 7 9 10 11 lif 15 16 17 19 20 21 23 2if 0.972 1.815 0.572 0.7*f1 0.850 0.6<f0 0.7 if 6 1.631 1.521 0.567 0.820 0.923 0.824 0.389 0*567 1.255 0.660 0.352 0. 359 WGT. AVG. STANDARD DEVIATION 0.527 0.65if 0.1*61 0. M+9 0.290 REGRESSION ZERO COEFF. GRADIENT CORRECTION 1.735 1.627 1.667 1 .974 1.681* •1.8<f5 •1.493 •1.806 •1.914 O.031* O.Olif 0.033 ■ 0.017 0.108 0.342 0.471 -0.233 -0.249 -0.195 -7.9 10.2 6.0 - 22.6 12.9 11.6 -35.6 0.4 22.4 -0.8 1.2 1.3 22.5 17.1 -15.2 -40.9 12.9 5.8 -6.4 EQUIVALENT RESISTANCE - COMPUTATION AND ERROR ANALYSIS STANDARD DEVIATION RESIST- COEFFI- ANCE ClENT EM F EQUIVALENT GRADIENT RESISTANCE LEVEL 3-4 3-5 2-3 1-4 DIFF. R U N 1 125.0 122.2 1.169 3.252 2.083 2 125.7 122.6 1.148 3.235 2.088 3 1 23.6 120.8 1.262 3.342 2.080 4 120.7 118.9 1.349 3.450 2.101 5 118.1 116.1 1.529 3.618 2.089 6 115.6 112.4 1.809 3.883 2.074 REGRESSION COEFFICIENT LEVEL 2-3 OBSERVED STA N D A RD DEVIATION 0,021 0.0054 0.0054 0.0056 0.0057 0.0061 0.0066 LEVEL 1-4 0.014 0.0301 0.0335 0.0268 0.0253 0.0235 0.0215 COMPUTED STANDARD DEVIATION 0 .0 1 1 113 TABLE 14A EXPERIMENTAL MEASUREMENTS FLUID - MERCURY SET 2 THERMOCOUPLE DATA LEVEL EMF, MICROVOLTS RUN 1 2 3 l» 5 6 7 NO. 3 1 1950.5 1952.2 1974.0 1977-8 1981.5 1985.6 1988.1 2 1954.6 19 56*. i f 1977.6 1981.9 1985.9 1990.0 1993.0 3 1954.0 1956.0 1977-6 1981.9 1985.9 1990.1 199 3.1 If 1955.2 1957.2 1979.0 1983.3 1987.4 1991.8 1994.8 5 1956.0 1957.3 1978.9 1983.1 1987*2 1991.5 1994.7 5 6 1760.8 1758.3 1792.9 1793.9 1794.9 1796.0 1797.0 7 1759.6 1757.0 1790.6 1791.5 1792.6 1794.0 1794.6 9 1757.9 1755.0 1789.7 1790.6 1791.6 1792.6 1793.5 10 1763.8 1761.1 1795.0 1796.0 1797.2 1798.5 1799.5 4 11 1861.0 1 860.4 1 887.9 1890.2 1 893.0 1 895*4 1 897.5 13 1 862.9 1 862.5 1 889.0 1 891.5 1 894.0 1 896.9 1 898.6 15 1 863.5 1 863.1 1888.8 1 892.6 1 894.8 1 897.6 1 899.4 1 16 2082,1 2080.1 20 83.5 2082.7 2082.0 2081.7 2081.6 17 2086.1 2084.3 2087.1 2086.7 2086.7 2085.5 2085*1 20 2077.9 2076.4 2080.1 2079.5 2078.5 2078.0 2077*4 2 21 2063.2 2061.4 2065.8 2065.1 2063.7 2062.7 2062.2 23 2060.0 2057.5 2062.7 2061.6 2060,6 2059.5 2059.1 24 2057.8 2055.5 2060.8 2059.6 2059.0 2057*6 2057.3 FILM THICKNESS (INCHES) 0 .1 3 4 8 0 .1 1 5 2 0 .0 8 4 6 0 .0 6 5 0 0 .0 4 4 8 0 .0 2 5 4 0 .0 1 4 7 114 TABLE 14B ANALYSIS OF EXPERIMENTAL DATA FLUID - MERCURY SET 2 THERMOCOUPLE EMF VS. GRADIENT ANALYSIS LEVEL THERMO EMF WGT• AVG. REGRESSION ZERO COUPLE STANDARD STANDARD COEFF. GRADIENT DEVIATION DEVIATION CORRECT 101 3 1 0.271 0.165 1.510 7.9 2 0.051 1.734 -0 .2 3 0.317 1.672 3.1 4 0.529 1.684 3.9 5 0.278 1.744 0 .6 5 6 0.391 0.135 -1.925 8 .8 7 0.137 -1.718 -4.5 9 0.209 - 1.964 7.7 10 0.185 -1.725 0.3 4 11 0.201 0.256 -0.003 1.9 13 0.498 0.181 -6 .8 15 0.487 0.315 -13.5 1 16 0.217 0.135 0.291 -5.4 17 0.283 0.315 -2.7 20 0.178 0.039 2.0 2 21 0.241 0.119 -0.169 1*4 23 O .090 -0.258 3.0 2 k 0.217 -0.268 1.6 EQUIVALENT RESISTANCE - COMPUTATION AND ERROR ANALYSIS EMF EQUIVALENT STANDARD DEVIATION GRAD 1 ENT RESISTANCE RESIST COEFFI ANCE CIENT LEVEL 3-4 3-5 2-3 1 4 DIFF. RUN 1 57.9 55.3 1.923 3.973 2.050 0.0043 0.0132 2 59.2 56.5 1.810 3.861 2.051 0.0041 0.0135 3 54.8 52.9 1.619 3.684 2.065 0.0043 0.0158 4 55.9 53.9 1.495 3.556 2.062 0.0041 0.0167 5 56.7 54.7 1.381 3.446 2.065 0.0040 0.0178 6 57.6 55.5 1.263 3.332 2.070 0.0039 O.OI99 7 58.2 56.1 1.190 3.258 2.068 0.0039 0.0231 REGRESSION COEFFICIENT LEVEL 2-3 LEVEL 1--4 OBSERVED STANDARD DEVIATION 0.0U4 0.006 COMPUTED STANDARD DEVIATION 0.0U7 115 TABLE 15A EXPERIMENTAL MEASUREMENTS FLUID - MERCURY SET 3 THERMOCOUPLE DATA LEVEL EMF, MICROVOLTS RUN 1 2 3 4 5 6 NO* 3 1 1702.1 1697*7 1693*4 1680.5 1670*0 1667*4 2 1706.7 1701*5 1697*0 1684*5 1674.0 1671*4 3 1707*1 1702.0 1697*1 1683*7 1672*7 1669*8 4 1710.1 1705*4 1700.0 1686*9 1675*5 1672*5 5 1711*4 1706.6 1701*0 1688*4 1676.9 1674.0 5 6 1415*1 1413*3 1412*0 1406*9 1 403*9 1402*9 7 1407*8 1405*9 1404.6 1403.0 1399*0 1398*3 10 1418.0 1415*1 1414*7 1410.0 1406.9 1406.0 4 11 1559*6 1553*7 1553*6 1545*6 1538*1 1536*1 13 1559*2 1554*6 1552*3 1548*0 1540.5 1538.6 15 1561*4 1557*8 1554*5 1548*7 1541.0 1539*0 1 16 1835*8 1840*3 1842*3 1835*6 1838*5 1838*6 17 1 840*7 1 845*4 1 847*4 1840*9 1 843*9 1 844*0 19 1836.9 1841*8 1843*8 1837*4 1840*2 1840*3 20 1 829*8 1 835*0 1 837*0 1829*9 1 833*5 1833*4 2 21 1806*9 1 812*4 1 814*8 1809*1 1813.0 1 813*1 23 1 802*0 1 807 *7 1 810*5 1805*0 1 808*9 1 809*1 24 1800*1 1806.4 1808*2 1802.9 1806.2 1806*9 FILM THICKNESS (INCHES) 0 .0 2 0 2 0 *0 4 0 2 0 * 0 6 0 2 0 .0 8 0 4 0 *1 1 9 9 0 .1 2 9 8 TABLE 15B ANALYSIS OF EXPERIMENTAL OAT A FLUID - MERCURY SET 3 THERMOCOUPLE EMF VS* GRADIENT ANALYSIS 116 LEVEL THERMO EMF WGT• AVG. REGRESSION ZERO COUPLE STANDARD STANDARD COEFF. GRADIENT DEVIATION DEVIATION CORRECTION 3 1 0.452 0.151 1.672 1.9 2 0.263 1.691 4.3 3 0.309 1.984 -19.6 4 0.306 2.036 -20.9 5 0.293 1.994 -16.1 5 6 0.651 0.307 -1.443 -23.8 7 0.446 -1.897 6 .8 10 0.442 -1.540 -13.2 4 11 0.942 0.465 -O.O77 5.1 13 0.831 -0.507 40.8 15 0.509 -0.162 14.5 1 16 0.241 0.105 0.264 -6.1 17 0.187 0.202 4.1 19 0.124 0.199 0.6 20 0.241 0.193 -5.8 2 21 0.073 0.156 -0.176 2.3 23 0.192 -0.285 6.7 24 0.353 -0.182 -3.6 EQUIVALENT RESISTANCE - COMPUTATION AND ERROR ANALYSIS EMF EQUIVALENT STANDARD DEVIATION GRADIENT RESISTANCE RESIST COEFFI ANCE CIENT LEVEL 3-4 3r~B 2-3 1-4 DIFF. RUN 1 83.2 83.9 1.138 3.286 2.148 0.0029 O.OI73 2 81.8 83.2 1.277 3.430 2.153 0.0030 0.0143 3 81.3 82.0 1.383 3.525 2.142 0.0031 0.0133 4 80.0 79.4 1.522 3.632 2.111 0.0033 0.0127 5 77.6 77.3 1.754 3.872 2.118 0.0036 0.0118 6 77.0 76.7 1.808 3.926 2.118 0.0036 0.0117 REGRESSION COEFFICIENT LEVEL 2-3 LEVEL 1-4 OBSERVED STANDARD DEVIATION 0.009 COMPUTED STANDARD DEVIATION 0 .0 0 6 0.012 TABLE 16A EXPERIMENTAL MEASUREMENTS FLUID - MERCURY SET THERMOCOUPLE DATA LEVEL EMF, MICROVOLTS RUN 1 2 3 4 5 NO* 3 1 1705.0 1700.2 1694.6 1676.0 1669.3 2 1709.6 1704.5 1699.1 1680.4 1673.9 3 1709.0 1704.0 1698.4 1678.9 1672.5 4 1712.4 1707.5 170U6 1681.7 1675.4 5 1715.0 1709.5 1703.5 1683.0 1677.5 5 6 141 If. 8 141 3.7 1412.0 1406.0 1403.5 7 1411.1 1408.5 1405.4 1401.2 1399.7 10 1419.1 1417.9 1415.9 1409.0 1406.8 4 11 1562.5 1559.5 1554.6 1542.0 1538.2 13 1562.9 1559.6 1554.7 1544.5 1540.2 15 1564.0 1561.1 1556.3 1545.1 1541.3 1 16 1837.1 1838.4 1840.5 1837.3 1837.6 17 1842.2 1843.3 1845.4 1842.8 1842.6 20 1829.9 1831.2 1833.7 1832.3 1832.0 2 21 1808.1 1809.6 1811.6 1811.7 1812.8 23 1803.6 1805.1 1807.3 1807.1 1807.8 24 1801.3 1802.9 1805.0 1804.6 1804.8 FILM THICKNESS ( INCHES) 0.0150 0.0300 0.0500 0.1000 0.1200 118 TABLE 16B ANALYSIS OF EXPERIMENTAL DATA FLUID - MERCURY SET 4 THERMOCOUPLE EMF VS. GRADIENT ANALYSIS LEVEL THERMO EMF WGT. AVG. REGRESSION ZERO COUPLE STANDARD STANDARD COEFF. GRADIENT DEVIATION DEVIATION CORRECT 101 3 I 0.295 0.135 1.659 2.5 2 0.263 1.653 7.5 3 0.222 1*798 -5.2 4 0.187 1.889 -9.4 5 0.423 1.973 -14.3 5 6 0.595 0.370 -1.735 -1.2 7 0.754 -1.824 1.2 10 0.535 -1.563 -11.4 4 11 0.280 0.230 0.110 -9.5 13 0.524 -0.222 18.5 15 0.286 -0.149 13.8 1 16 0.279 0.145 0.341 -11.8 17 0.127 0.305 -3.8 20 0.280 0.041 6.2 2 21 0.325 0.139 -0.301 12.8 23 0.140 -0.238 3.1 24 0.147 -0.148 -6.6 EQUIVALENT RESISTANCE - COMPUTATION A N D ERROR ANALYSIS EMF EQUIVALENT STANDARD DEVIATION GRAD 1 ENT RESISTANCE RESIST COEFFI ANCE CIENT LEVEL 3-4 3-5 2-3 1-4 DIFF. RUN 1 84.2 84.3 1.117 3.242 2.125 0.0027 0.0189 2 83.4 83.3 1.209 3.331 2.123 0.0028 0.0150 3 81.9 82.3 1.318 3.457 2.139 0.0030 0.0136 4 78.7 78.4 1.630 3.744 2.114 0.0034 0.0123 5 77.6 77.2 1.745 3.853 2.108 0.0036 0.0120 REGRESSION COEFFICIENT LEVEL 2-3 LEVEL 1--4 OBSERVED STANDARD DEVIATION 0.005 0.006 COMPUTED STANDARD DEVIATION 0 .007 119 TABLE 17A EXPERIMENTAL MEASUREMENTS FLUID - MERCURY SET 5 THERMOCOUPLE DATA LEVEL EMF, MICROVOLTS RUN 1 2 3 A 5 6 7 3 NO. 3 1 1808.9 180 U. 2 1 803.0 1795.6 1789.4 1784.4 1781.8 1795*9 2 1812.9 1808.5 1806.7 1799.3 1793.1 1788.1 1784.5 1799*7 3 1810.6 1806*3 1804.5 1796.8 1789.3 1785.5 1782.5 1797*8 4 1 814.2 1 809*9 1 807*8 1 800.0 1793.0 1789*1 1785*6 1 801.1 5 1815.6 1810.1 I808.6 1801.1 1794.6 1790.3 1786.0 1801.2 5 6 1437*5 1 436.5 1 437*1 1432.9 1430.9 1429.6 1 427.9 1432.8 7 1431*4 1430.1 1430.8 1426.4 1424.6 1422*5 1421.1 1425.8 9 1430.2 1 429.1 1429*9 1 425*7 1 424.0 1422.6 1420.9 1425.5 10 1441.0 1439.6 1440.5 1436.0 1434.4 1433.0 1431.0 1436.0 4 11 1624.1 1619.6 1620.0 1614.3 1610.4 1607*8 1604.3 1614.4 13 1626.6 1622.9 1622.9 1616.9 1613.0 1610.3 1607*0 1617*0 14 1625*7 1622.1 1621.9 1616.0 1612.0 1609*4 1606.0 1616.0 15 1627.6 1624.3 1623*7 1617*9 1613*9 1611.4 1607.8 1618.0 1 16 1994.2 1991.6 1995*6 1993.4 1991.2 1992.6 1992.0 1990.7 17 2001.7 2000.6 2003.0 2000.6 1998*5 1999.6 1998.9 1998.2 19 1999.0 1998.5 2000.0 1997.8 1996.0 1996*7 1996.5 1995.5 20 1992.0 1991*0 1992.8 1990*5 1988.7 1989*4 1989*3 1988.3 2 21 1959.7 1959.1 1960.5 1960.1 1959.1 1959*9 1960.2 1957*8 23 1953*6 1953.1 1954.9 1954.6 1953.0 1953*8 1954.0 1951.6 24 1950.4 1948.8 1951.2 1950.9 1949*6 1950.4 1950.8 1948.4 FILM THICKNESS (INCHES) 0 .0 5 0 0 0 .0 6 0 0 0 .0 7 0 2 0 .0 7 9 9 0 .0 9 0 3 0 .1 0 0 1 0 .1 1 0 0 0 .0 7 5 1 TABLE 17B 120 ANALYSIS OF EXPERIM ENTAL D A TA FLUID - M ERCU RY SET 5 THERM OCOUPLE EM F VS. GRADIENT ANALYSIS LEVEL THERM O EM F W GT. AVG. COUPLE STA N D A RD STA N DARD DEVIATION DEVIATION 3 1 0.334 0.161 2 0.279 3 0.481 4 0.342 5 0.297 5 6 0.217 0.100 7 0.257 9 0.136 10 0.088 4 11 0.454 0.159 13 0.216 14 0.217 15 0.249 1 16 0.611 0.217 17 0.326 19 0.349 20 0.269 2 21 0.328 0.186 23 0.262 24 0.363 EQUIVALENT RESISTANCE - COM PUTATION REGRESSION ZERO COEFF. GRADIENT CORRECTION 1*555 1*739 1.828 1.857 1.839 -1.752 -1.626 ■1.83** •1.740 ■0.077 ■0.027 •0.010 0.011 0.125 0 .344 0.348 0.363 ■0.297 •0.257 ■0.331 16.9 1.3 -10.5 - 10.1 -7.3 2.1 -17.7 3.5 4.1 .3 .8 2.0 1.8 - 10.8 - 13.8 - 22.6 16.0 5.8 10.1 I : EM F G R A D I ENT EQUIVALENT RESISTANCE LEVEL 3-4 RU N 3-5 2-3 1 2 3 4 5 6 I 108.5 107.0 106.6 105.7 104.5 103.9 102.9 105.9 107.8 106.8 106.1 105.2 103.8 103.0 102.5 105.4 1.319 1.366 1.408 1.489 1.561 1.624 1.668 1.456 1-4 3.440 3.495 3.541 3.606 3.674 3.738 3.785 3.575 STA N D ARD DEVIATION RESIST- COEFFI- A N CE CIENT 0.0113 0.0109 0.0106 0.0101 0.0098 0.0095 0.0093 0 .0 1 0 3 REGRESSION COEFFICIENT DIFF. 2.121 0.0024 2.129 0.0024 2.133 0.0024 2.117 0.0025 2.113 0.0025 2.114 0.0025 2.117 0.0026 2.119 0.0025 2-3 LEVEL 1-4 OBSERVED STANDARD DEVIATION 0.012 COM PUTED STANDARD DEVIATION 0.004 0.007 TABLE 18A EXPERIMENTAL MEASUREMENTS FLUID - NUJOL SET 1 THERMOCOUPLE DATA LEVEL EMF, MICROVOLTS RUN 1 2 3 4 5 6 NO. 3 1 1234.3 1266.5 1300.0 1348.5 1422.6 1825.2 2 1233.4 1265.5 1299.4 1348.5 1423.9 1837*4 3 1232.6 1264.8 1298.3 1347.3 1421.0 1837.2 4 1233.6 1265.8 1299.5 1348*7 1422.2 1838.4 5 1234.9 1267.2 1301.0 1349.9 1424.0 1832.1 5 6 1105.4 1121.3 1132.3 1148.9 1173.3 1305.0 7 1102.9 1118.6 1129.4 1145.5 1169.0 1295.5 9 1103.0 1118.0 1129.0 1144.6 1167.6 1 293.2 10 1107.2 1123.6 1135.0 1152.0 1176.7 1301.1 4 11 1171.5 1195.0 1217.4 1250.2 1299.1 1562.5 12 1171.4 1195.0 1217.6 1250.3 1299.7 1568.9 14 1170.6 1194.4 1216.9 1249*4 1298.8 1568.2 15 1170.7 1194.7 1217*3 1249.6 1297*6 1567.6 1 16 2158.0 2153*7 2148.6 2141.0 2129.3 2072.3 18 2160.1 2156.4 2152.0 2144.5 2133.1 2073.0 19 2162.0 2157.8 2153.4 2146.5 2135*9 2080.1 20 2154.4 2150.1 2145.0 2136.8 2124.0 2059*2 2 21 2145*4 2139.8 2132.8 2122.3 2105.6 2018.6 22 2144.3 2139*0 2131*5 2120.1 2102.2 2005.4 24 2142,7 2136.3 2128.5 2116.6 2098.2 2003.4 25 2135*2 2128.1 2119*5 2106.6 2086.8 1991.0 FILM THICKNESS (INCHES) 0.0614 0.0513 0.0412 0.0313 0.0210-0. TABLE 18B ANALYSIS OF EXPERIMENTAL DATA FLUID - NUJOL SET 1 THERMOCOUPLE EMF VS. GRADIENT ANALYSIS LEVEL THERMO EMF WGT. AVG. REGRESSION ZERO COUPLE STANDARD STANDARD COEFF. GRADIENT DEVIATION DEVIATION CORRECTION 3 1 0.860 0.322 1.671 3.7 2 0.283 1.789 -2.5 3 0.836 1.794 -4.0 4 0.759 1.795 -2.9 5 0.426 1.726 1.9 5 6 0.410 0.363 -1.698 -2.2 7 0.259 -1.759 -2.2 9 0.555 -1.777 -1.9 10 1.052 -1.753 3.2 4 11 0.676 0.262 -0.049 3.9 12 0.171 0.008 1.1 14 0.119 0.009 0.4 15 0.533 0.000 0.8 1 16 0.397 0.211 0.233 -1.3 18 0.560 0.215 2.6 19 0.355 0.264 2.0 20 0.165 0.147 -1.1 2 21 0.204 0.470 -0.125 -0.0 22 0.762 -0.234 3.7 24 0.232 -0.231 0.7 25 1.288 -0.268 -6.5 EQUIVALENT RESISTANCE - COMPUTATION AND ERROR ANALYSIS EMF EQUIVALENT STANDARD DEVIATION GRADIENT RESISTANCE RESIST COEFFI ANCE CIENT LEVEL 3-4 3-5 2-3 1-4 DIFF. RUN 1 36.4 36.9 24.622 26.809 2.187 0.0937 1.4702 2 41.0 41.6 20.918 23*110 2.192 0.0710 1.3205 3 47*5 48.0 17.242 - 19*433 2.191 0.0511 1.1722 4 56.7 57.3 13.385 15.577 2.192 0.0338 1.0426 5 70.9 71.7 9.418 11.615 2.197 0.0198 0.9951 6 151.0 152.9 1.114 3.306 2.192 0.0039 0. REGRESSION COEFFICIENT LEVEL 2-3 LEVEL 1-4 OBSERVED STANDARD DEVIATION 0.169 0.171 COMPUTED STANDARD DEVIATION 0.542 123 TABLE 19A EXPERIMENTAL MEASUREMENTS FLUID - NUJOL SET 2 THERMOCOUPLE DATA LEVEL EMF, MICROVOLTS RUN 1 2 3 4 5 6 7 NO, 3 1 1240.2 1219.2 1239*3 1264.0 1298.4 1345*1 1220.2 2 1 239*4 1 218.5 1 238.8 1 263*5 1 298.1 1345*3 1 219*4 3 1 239*0 1 218.1 1238.0 1 262.7 1 297.0 1 343*9 1218.9 4 1240.2 1219*4 1239*3 1264.1 1298.4 1345*4 1220.2 5 1241.9 1220.9 1241.0 1265.8 1300.2 1347.2 1221.7 5 6 1116.5 1108.3 1114.6 1122.7 1133*2 1149*0 1109*0 7 1110.8 1104.0 1110.6 1117*6 1128.5 1143*3 1104*3 9 1112.5 1105.3 1111*7 1119*4 1130.0 1145*0 1106.1 10 1116.0 1108.4 1115*0 1123*2 1134.7 1150.4 1108.9 4 11 1177*9 1163*6 1176.8 1193.0 1215*9 1246.5 1164.4 13 1177.1 1163.0 1176.0 1192.3 1215*1 1246.0 1163*5 14 1178.8 1164.8 1177*6 1193*7 1216.6 1247*3 1165*6 15 1176*4 1162.5 1175*5 1191*6 1214.4 1245*3 1163*2 1 16 2162.4 2165*4 2161.9 2157*1 2150.5 2141.8 2165*8 18 2159.6 2163.0 2159*2 2154.0 2147*0 2137*0 2163*5 19 2162.4 2165*7 2162.3 2157*1 2150.8 2142.3 2166.0 20 2156.4 2159*7 2156.1 2150.5 2143*3 2133*1 2160.3 2 21 2146.8 2151*8 2146*8 2140.0 2131*1 2119*4 2152.0 22 2146.2 2151.1 2146.0 2138.9 2129.0 2116.0 2151.6 23 2145.6 2150.7 2145.5 2138.4 2128.5 2115*2 2151.1 FILM THICKNESS (INCHES) 0 .0 6 1 1 0.0711 0 .0 6 0 9 0 .0 5 1 0 0 .0 4 0 8 0 .0 3 1 6 0.0711 TABLE 19B 124 ANALYSIS OF EXPERIMENTAL DATA LEVEL FLUID - NUJOL SET 2 THERMOCOUPLE EMF VS. GRADIENT ANALYSIS THERMO EMF WGT• AVG. REGRESSION ZERO COUPLE STANDARD STANDARD COEFF. GRADIENT DEVIATION DEVIATION CORRECTION 1 0.065 0.034 1.744 0.1 2 0.105 1.781 -1.9 3 0.062 1.742 -1 .0 4 0.066 1.751 -0.1 5 0.068 1.762 1.1 6 0.361 0.137 -1.746 1.6 7 0.283 -1.785 -1.7 9 0.133 -1.777 -0.5 10 0.078 -1.675 -0.8 11 0.129 0.065 -0.008 0.9 13 0.090 0.001 -0.2 14 0.170 -0.023 2.4 15 0.096 -0.011 -0.3 16 0.103 0.068 0.244 0.2 18 0.135 0.151 0.9 19 0.149 0.254 0.1 20 0.149 0.120 -1.3 21 0.187 0.081 -0.110 -2.2 22 0.080 -0.228 1.2 23 0.105 -0.239 1.1 EQUIVALENT RESISTANCE - COMPUTATION AND ERROR ANALYSIS EMF GRADIENT EQUIVALENT RESISTANCE LEVEL 3-4 RUN 1 35.5 2 3 1 .8 3 35.5 4 1*0*3 5 47.1 6 55.9 7 31.9 y $ 2-3 1-4 DIFF. STANDARD DEVIATION RESIST- COEFFI- ANCE ClENT 36.0 25.135 27.290 2.156 32.2 28*94 3 31.090 2.146 36.1 25.133 27.286 2.153 40.9 21.377 23.529 2.151 47*6 17.440 19.589 2.149 56.7 1 3.607 1 5.7 5 8 2.151 32.3 28.855 31.003 2.148 REGRESSION COEFFICIENT OBSERVED STANDARD DEVIATION COMPUTED STANDARD DEVIATION LEVEL 2-3 0.127 0.181 0.0283 0.0364 0.0282 0.0212 0.011*9 0.0098 0.0362 LEVEL 1-4 0.128 0.4767 0.5133 0.4766 0.4510 0.4455 0.4780 0.5122 TABLE 20A EXPERIMENTAL MEASUREMENTS FLUID - NUJOL SET THERMOCOUPLE DATA LEVEL EMF, MICROVOLTS RUN 1 2 3 4 5 NO. 3 1 1784.4 1422.7 1346.2 1299.5 1266.6 3 1788.9 1420.2 1344.2 1295*2 1264.1 4 1795*9 1421.7 1345*8 1296.7 1265*1 5 1796.5 1424.2 1348.4 1299*7 1268.3 5 6 1295*5 1176.0 1150.5 1134.0 1123*4 7 1287*0 1171*5 1147.3 1131.5 1121.3 9 1286.6 1171*5 1147*3 1131*6 1121.0 10 1302.9 1179.7 1154.0 1137*3 1126.4 4 11 1534*1 1298.8 1248.9 1217*4 1196.2 13 1538.9 1298.8 1248.0 1216.5 1195*0 14 1543.0 1300.7 1250.0 1218.6 1196.7 15 1543*6 1300.9 1249.6 1218.0 1196.3 1 16 1996.6 2093*0 2113*1 2126.5 2135*0 18 1984.1 2084.2 2108.0 2122.7 2130.8 19 2000.0 2096.6 2117*0 2130.0 2138.3 20 1972.6 2074.2 2100.0 2115.0 2124.1 2 21 1970.6 2082.4 2106.2 2121.0 2130.5 22 1935*0 2064.3 2091.6 2109*1 2120.1 23 1928.4 2055.6 2084.6 2102.0 2113*9 24 1915*9 2045.0 2075*1 2092.9 2105*6 FILM THICKNESS (INCHES) 0. 0.0215 0.0319 0.0421 0.0516 TABLE 20B 126 ANALYSIS OF EXPERIMENTAL DATA FLUID - NUJOL SET 3 THERMOCOUPLE EMF VS. GRADIENT ANALYSIS LEVEL THERMO EMF WGT• AVG. REGRESSION ZERO COUPLE STANDARD STANDARD COEFF. GRADIENT DEVIATION DEVIATION CORRECTION 3 1 0.909 0.357 1.682 3.8 3 0.388 1.761 -3;1 4 0.699 1.820 -4.9 5 0.656 1.795 -0.7 5 6 0.149 0.108 -1.716 -1.7 7 0.244 -1.779 -1.4 9 0.135 -1.782 -1.2 10 0.271 -1.673 -0.6 4 11 0.582 0.207 -0.087 5.3 13 0.334 -0.026 1.3 14 0.285 -0.003 2.0 15 0.303 0.008 1.1 1 16 0.772 0.485 0.232 1.0 18 0.630 0.146 0.3 19 0.838 0.230 4.6 20 1.328 0.103 -5.4 2 21 0.810 0.383 0.017 5.7 22 0.664 -0.231 5.2 23 0.458 -0.229 -2.0 ?4 0.947 -0.267 -9.3 EQUIVALENT RESISTANCE - COMPUTATION AND ERROR ANALYSIS EMF EQUIVALENT STANDARD DEVIATION GRADIENT RESISTANCE RESIST COEFFI ANCE CIENT LEVEL 3-4 3-5 2-3 1-4 DIFF. RUN 1 138.2 142.3 1.019 3.167 2.148 0.0038 0. 2 69.0 70*7 9.034 11.170 2.136 0.0155 0.8741 3 54.4 56. 1 13.235 15.385 2.150 0.0269 0.8706 4 45.7 46.9 17.222 19.373 2.151 0.0408 0.9559 5 39.4 40.8 20.826 22.979 2.153 0.0560 1.0596 REGRESSION COEFFICIENT LEVEL 2-3 LEVEL 1-4 OBSERVED STANDARD DEVIATION 0.123 COMPUTED STANDARD DEVIATION 0.472 0 .1 3 0 TABLE 21A EXPERIMENTAL MEASUREMENTS FLUID - NUJOL SET if THERMOCOUPLE DATA LEVEL EMF, MICROVOLTS RUN 1 2 3 NO,> 3 1 1 if02 • 7 1400.8 1332.2 2 1if05.1 1402.5 1333.3 3 1ifO3.0 1400.4 1331.1 if 1405.0 1402.1 1332.1 5 1if06.8 1404.2 1334.4 5 6 1157.1 1155.5 1133.1 7 1153.0 1151.6 1130.0 8 1153.0 1151.9 1129.8 9 1161.3 1160.1 1136.8 if 11 1281.0 1278.6 1232.9 13 1281.5 1278.4 1232.8 lif 1285.1 1281.9 1235.9 15 1283.7 1280.3 1234.5 1 16 2093.2 2092.3 2112.1 18 2085.6 2086.7 2106.1 19 2096.6 2096.4 2115.2 20 2075.3 2076.7 2097.5 2 21 2082.5 2083.5 2103.9 22 2065*1 2065.5 2089.4 23 2055.8 2060.6 2083.6 25 20if5.6 2045.4 2072.2 FILM THICKNESS (INCHES) 0 .0 2 1 S 0 .0 2 1 2 0 .0 3 1 8 0 .0 lf1 7 0 .0 5 1 6 0 . TABLE 21B ANALYSIS OF EXPERIMENTAL DATA FLUID - NUJOL SET 4 THERMOCOUPLE EMF VS. GRADIENT ANALYSIS 128 LEVEL THERMO- EMF COUPLE STANDARD DEVIATION WGT. AVG. STANDARD DEVIATION REGRESSION ZERO COEFF. GRADIENT CORRECTION 1 1*331 0.452 1*577 8.8 2 0*365 1.720 1.8 3 0.760 1.792 -4.4 4 1*012 1.860 -7.1 5 1.011 0.189 1.839 -3.6 6 0.364 -1.725 -1.2 7 0.361 -1.788 -0.8 8 0.245 -1.789 -0.8 9 0.469 -1.675 -0.7 11 0.758 0.477 0.304 -0.067 3.7 13 -0,009 0.2 14 0.603 0.004 2.7 15 0.516 0.019 0.5 16 0.707 0.400 0.236 0.6 18 0.127 0.149 0.2 19 0.699 0.241 3.5 20 1.019 0.106 -5.9 21 0.982 0.589 0.029 4.5 22 0.944 -0.230 5.2 23 1.417 -0.254 1.1 25 1*237 -0.277 -9.2 EQUIVALENT RESISTANCE - COMPUTATION AND ERROR ANALYSIS EMF EQUIVALENT STANDARD DEVIATION GRADIENT RESISTANCE RESIST COEFFI ANCE CIENT LEVEL 3-4 3-5 2-3 1-4 DIFF. RUN 1 70.5 70.9 9.254 11.376 2.122 0.0211 1.0348 2 69.5 70.6 9.356 11.479 2.123 0.0213 1.0408 3 56.2 57.2 13.179 15.321 2.142 0.0348 1.0755 4 47.5 48.3 16.911 19.049 2.138 0.0514 1.1920 5 40.3 41.5 20.815 22.976 2.161 0.0724 1.3446 6 139.2 141.7 1.059 3.199 2.140 0.0053 0. REGRESSION COEFFICIENT LEVEL 2-3 LEVEL 1--4 OBSERVED STANDARD DEVIATION 0. 106 0.104 COMPUTED STANDARD DEVIATION 0. 511 129 TABLE 22A EXPERIMENTAL MEASUREMENTS FLUID - GLYCEROL SET 1 THERMOCOUPLE DATA LEVEL EMF, MICROVOLTS RUN 1 2 3 4 5 6 NO* 3 1 1258.5 1300.9 1359.6 1412.4 1473.1 1559*6 2 1259*0 1301.7 1361.2 1414.3 1476.0 1564.5 3 1256.9 1299*5 1359*0 1412.1 1473*6 1562.3 4 1259*0 1302.1 1361.6 1415*0 1476*8 1566.0 5 1260.7 1304.2 1363.8 1417*1 1479*0 1568.1 5 6 1059*5 1073*6 1093.1 1111.3 1131*4 1162.4 7 1057*2 1070*7 1089*4 1106.0 1125*5 1155*8 9 1055*7 1069*3 1088.0 1106.1 1125*4 1155*2 10 1062.7 1077*1 1096.9 1115*6 1136.3 1168.0 4 11 1161.9 1190.5 1229*5 1263*3 1304*1 1362.4 12 1160.4 1188.7 1227*7 1261.1 1301.8 1360.4 13 1162.5 1191*0 1230.6 1264.2 1305*3 1364*8 15 1162.8 1191*5 1231*1 1264*5 1305*6 1365*3 1 16 2077*3 2072.0 2063*6 2051*1 2048.8 2035*8 17 2082.9 2078.3 2070.8 2065*1 2057*3 2044.6 20 2073.0 2067*2 2058.5 2051.6 2043*0 2028.4 2 21 2059*0 2051*1 2039*0 2029.4 2017*4 1997*9 23 2057*3 2049*4 2035*9 2025*6 2012.4 1991*9 24 2053*8 2045*6 2032.1 2021.7 2008.1 1987.8 FILM THICKNESS (INCHES) 0 .0 7 6 0 0 .0 6 1 3 0 .0 4 5 8 0 .0 3 5 4 0 .0 2 5 9 0 .0 1 6 2 7 him :;yj 1786.9 1241*7 1232.5 1231.7 1248.4 1508.0 1506.4 1513*0 1513*8 2005*7 2017*0 1998.7 1955*4 1943*7 1940.1 o . TABLE 22B ANALYSIS OF EXPERIMENTAL DATA FLUID - GLYCEROL SET 1 THERMOCOUPLE EMF VS. GRADIENT ANALYSIS LEVEL THERMO EMF WGT. AVG. REGRESSION ZERO COUPLE STANDARD STANDARD COEFF. GRADIENT DEVIATION DEVIATION CORRECTION 3 1 0.935 0.287 1.666 4.3 2 0.211 1.775 -2.5 3 0.520 1.786 -5.6 4 0.592 1.814 -5.1 5 0.438 1.782 -0.6 5 6 0.199 0.155 -1.713 -2.5 7 0.290 -1.784 -1.1 9 0.408 -1.776 -2.6 10 0.260 -1.676 -1.4 4 11 0.396 0.217 -0.051 5.5 12 0.317 -0.051 3.7 13 0.421 -0.006 2.9 15 0.541 -0.002 3.0 1 16 2.194 0.953 0.199 -2.4 17 0.500 0.248 1.8 20 0.579 0.163 -3.9 2 21 0.451 0.333 -0.135 -0.4 23 0.693 -0.237 4.4 24 0.534 -0.238 0.6 EQUIVALENT RESISTANCE - COMPUTATION AND ERROR ANALYSIS EMF EQUIVALENT STANDARD DEVIATION GRADIENT RESISTANCE RESIST COEFFI ANCE CIENT LEVEL 3-4 3 rS 2-3 1-4 DIFF. RUN 1 55.4 57.1 13.908 16.125 2.217 0.0240 0.2995 2 63.7 65.4 11.371 13.570 2.199 0.0176 0.2750 3 75.1 76.9 8.732 10.926 2.194 0.0121 0.2608 4 84.0 86.9 6.994 9.179 2.185 0.0091 0.2663 5 95.9 98.8 5.399 7.598 2.199 0.0068 0.2969 6 112.0 115.3 3.687 5.884 2.197 0.0049 0.4002 7 151.2 155.5 1.027 3.228 2.202 0.0029 0. REGRESSION COEFFICIENT LEVEL 2-3 LEVEL 1-4 OBSERVED STANDARD DEVIATION 0.034 0.040 COMPUTED STANDARD DEVIATION 0 .1 2 4 TABLE 23A EXPERIMENTAL MEASUREMENTS FLUID - GLYCEROL SET THERMOCOUPLE DATA LEVEL EMF, MICROVOLTS RUN 1 2 3 4 5 NO. 3 1 1712.5 1497.0 1422.6 1372*9 1333.3 2 17 22.0 1503*0 1 428.0 1 378*0 1 339*0 3 1717.4 1497*7 1422.4 1372*5 1332.8 4 1721.7 1500.6 1425*0 1374*7 1334*9 5 1722.9 1502.6 1427*0 1376*6 1336.5 5 6 1 307*4 1 235*2 1 210.5 1193*4 1178.6 7 1300.6 1230.8 1207*0 1190*6 1176.8 9 1300.5 1230.9 1207*0 1190*6 1176.8 10 1 312.8 1 238.7 1 213*1 1195*9 1180.8 4 11 1511.5 1368*1 1318.8 1285*0 1258.3 13 1 514.6 1 369*3 1 319*8 1 286*3 1 259*6 14 1515*7 1370*4 1320.6 1287*0 1260.2 15 1514.6 1369*2 1319*3 1285*6 1258.4 1 16 2087.5 2132*7 2150.0 2160.0 2168.4 18 2074.6 2125*7 2143*9 2155*0 2164.1 19 2089*4 2135*0 2151*9 2162*0 2170.2 20 2063*9 2117*4 2136.8 2148*9 2158.5 2 21 2054.6 2113*4 2133*4 2146*5 2156.4 22 2032*6 2099*0 2122.7 2138*0 2149*0 23 2022.3 2091*0 2116.6 2132*3 2144*1 25 2009.0 2079*5 2106.1 2122.7 2135*5 FILM THICKNESS (INCHES) 0.0105 0.01*03 0.0611 0.0812 0.1011 TABLE 23B ANALYSIS OF EXPERIMENTAL DATA FLUID - GLYCEROL SET 2 THERMOCOUPLE EMF VS. GRADIENT ANALYSIS LEVEL THERMO EMF WGT. AVG. REGRESSION ZERO COUPLE STANDARD STANDARD COEFF. GRADIENT DEVIATION DEVIATION CORRECTION 3 1 0.421 0.131 1.685 0.6 2 0.303 1.743 2.9 3 0.190 1*762 -3.9 4 0.214 1.792 -3.2 5 0*123 1.785 -0.9 5 6 0.155 0.073 -1.727 -1.3 7 0.160 -1.792 -0.6 9 0.122 -1.793 -0.5 10 0.143 -1.683 - 1.2 4 11 0.338 0.117 -0.030 2.3 13 0.178 -0.004 2.0 14 0.074 0.003 2.4 15 0.134 0.010 0.5 1 16 0.233 0.116 0.282 -0 .2 18 0.313 0.166 1.0 19 0.092 0.283 1.7 20 0.107 0.096 -1.7 2 21 0.568 0.252 -0.003 1.1 22 0.265 -0.206 2.7 23 0.307 -0.279 0.9 25 0.642 -0.339 -5.5 EQUIVALENT RESISTANCE - COMPUTATION AND ERROR ANALYSIS EMF EQUIVALENT STANDARD DEVIATION GRADIENT RESISTANCE RESIST COEFFI LEVEL 3-4 3-5 RUN 1 117*1 118.2 2-3 2.619 1-4 DIFF. 4.791 2.172 ANCE 0.0026 CIENT 0.5426 2 75*4 76.0 7.823 9.996 2.173 0.0058 0.1837 3 61.1 61.6 11.272 13.444 2.171 0.0091 0.1630 4 51*5 52.1 14.583 16.752 2.169 0.0132 0.1670 5 44.4 44.8 18.067 20.243 2.176 0.0184 0.1804 REGRESSION COEFFICIENT LEVEL 2-3 LEVEL 1 -if OBSERVED STANDARD DEVIATION 0 .0 8 1 0 .0 8 3 COMPUTED STANDARD DEVIATION 0 .1 2 9 TABLE 24A EXPERIMENTAL MEASUREMENTS FLUID - MERCURY-WATER SET THERMOCOUPLE DATA LEVEL RUN 1 2 NO. 3 1 1580.5 1546.9 2 1586.3 1551.6 3 1583.5 15^8.7 4 1587.5 1552.1 5 1591.2 1556.1 5 6 1229.2 1218.0 7 1221.2 1210.7 9 1222.3 1211.7 10 1234.1 1223.0 4 11 1405.6 1382.5 13 1407.6 1384.6 15 1406.2 1383.0 1 16 2082.5 2089*6 17 2072.8 2080.9 18 2083.9 2091.4 19 2064.9 2073.0 2 21 2051.1 2060.6 22 2037.0 2047.5 23 2031.0 2041.8 25 2022.0 2032.6 FILM THICKNESS (INCHES) 0 .1 6 2 1 0.1721 EMF, MICROVOLTS 3 4 5 1619.0 1671*2 1517.4 1626.0 1676.4 1519*8 1623.4 1675.6 1 518*7 1628.0 1680*5 1521.9 1632.0 1691.1 1526.4 1242.3 1258.5 1206.4 1233.8 1251.0 1201.1 1234.9 1251.1 1201.1 1247*9 1265.3 1211.9 1431.5 1468.8 1364.1 1433.9 1468.1 1364*5 1432.2 1470.3 1365*8 2074.3 2063.7 2096.2 2062.9 2051.1 2087*9 2074.3 2065.1 2098.2 2054.0 2041.6 2079.5 2039.6 2025.3 2068.8 2024.4 2008.9 2056.6 2018.0 2002.5 2050*7 2008.9 1993*4 2042.0 0 .1 5 2 4 0 .1 4 2 5 0 .1 8 2 5 TABLE 24B ANALYSIS OF EXPERIMENTAL DATA FLUID - MERCURY-WATER SET 1 THERMOCOUPLE EMF VS* GRADIENT ANALYSIS LEVEL THERMO EMF WGT* AVG. REGRESSION ZERO COUPLE STANDARD STANDARD COEFF. GRADIENT DEVIATION DEVIATION CORRECTION 3 1 0*303 0.577 1*606 *•4 2 1.693 1.698 4*8 3 0*610 1.719 0*6 4 0.733 1*780 -1*6 5 1.569 1.960 -15.0 5 6 0*860 0*294 -1.728 -0.5 7 0*233 -1.793 -1.0 9 0*425 -1.795 -0.2 10 0*352 -1*681 0*2 4 11 0*962 0.698 0*008 -1.2 13 0*512 -0*029 3.9 15 1.585 0*011 -0.5 1 16 0*334 0*233 0*290 ~ 2 * l 17 0.071 0*140 2.8 18 0.573 0*255 2*3 19 0*486 0*094 -1.0 2 21 0.167 0*063 -0.078 3.4 22 0*080 -0.216 3.6 23 0*110 -0.239 -0.2 25 0*113 -0.247 -8.3 EQUIVALENT RESISTANCE - COMPUTATION AND ERROR ANALYSIS EMF EQUIVALENT STANDARD DEVIATION GRADIENT RESISTANCE RESIST COEFFI ANCE CIENT LEVEL 5-4 3-5 2-3 1-4 DIFF. RUN 1 101*5 102*5 4*383 6*533 2*150 0.0097 0.1772 2 94.5 95.7 5.166 7.320 2*154 0*0117 0*1805 3 108*9 110*2 3.603 5.755 2.152 0*0080 0*1779 4 120*1 120*6 2*724 4.863 2*140 0*0064 0*1870 5 90.1 90*2 5.920 8*053 2*133 0*0137 0.1853 REGRESSION COEFFICIENT LEVEL 2-3 LEVEL 1-4 OBSERVED STANDARD DEVIATION 0 *0 5 5 0 *0 6 5 COMPUTED STANDARD DEVIATION 0*081 TABLE 25A EXPERIMENTAL MEASUREMENTS FLUID - MERCURY-WATER SET THERMOCOUPLE DATA LEVEL EMF, MICROVOLTS RUN 1 2 3 4 5 NO. 3 1 1591.0 1524.9 1553.4 1628.4 1677*4 2 1593.1 1525*8 1554.6 1631.2 1681.1 3 1590.5 1523.0 1551*7 1628.1 1678.2 4 1593.4 1525.6 1554.4 1631*1 1681.3 5 1596.4 1529.1 1557*5 1633.9 1683.8 5 6 1234.8 1211.0 1220.2 1244*9 1261.0 7 1229*0 1205.9 1214.8 1238*5 1254.1 9 1228.8 1205.6 1214.4 1238.0 1253*5 10 1240.0 1215.8 1225.1 1250.5 1267*1 4 11 1413*4 1 368.1 1386.5 1 435.9 1468.4 12 1416.0 1 370.7 1 389.2 1 439.5 1 472.5 15 1416.6 1 371.2 1 389.8 1 440.0 1 472.9 1 16 2098.5 2109*6 2104.2 2091.0 2082.1 18 2093.9 2105*9 2100.1 2085*5 2075.6 19 2101.5 2112.8 2106*8 2093.4 2084.1 20 2088.3 2100.8 2094.7 2080.4 2070.6 2 21 2059.0 2075*3 2067*2 2048.9 2035*7 22 2053*9 2071.4 2062.7 2042.5 2028*5 24 2053.0 2070.4 2061.8 2041.4 2028.0 25 2040*9 2058.5 2049*7 2028.8 2015*0 FILM THICKNESS (INCHES) 0 .1 6 3 5 0 .1 8 3 7 0 .1 7 3 5 0.1531 0 .1 4 2 9 TABLE 25B ANALYSIS OF EXPERIMENTAL DATA 136 LEVEL A 1 FLUID - MERCURY-WATER SET 2 THERMOCOUPLE EMF VS. GRADIENT ANALYSIS THERMO EMF WGT. AVG. REGRESSION ZERO COUPLE STANDARD STANDARD COEFF. GRADIENT DEVIATION DEVIATION CORRECTION 1 0.26if 0.083 1.685 if* 5 2 0.185 1*781 -3.4 3 0.031 1.775 -5.7 i f 0.056 1.792 -4.6 5 0.082 1.762 1.6 6 O.llif 0.054 - 1.721 -2.1 7 0.090 - 1.782 - 1.6 9 0.053 -1.792 - 1.0 10 0.139 -1.676 -1.4 11 0.30if 0.130 -0.050 4.3 12 0.111 0.003 1.9 15 0.077 -0.001 2.9 16 0.13if 0.083 0.266 -2.4 18 0.187 0.172 2.5 19 0.171 0.231 3.9 20 0.165 0.180 -3.6 21 0.250 0.093 -0.1 2l f -1.7 22 0.106 -0.238 4.7 2i f 0.1 if9 -0.226 2.6 25 0.172 -0.263 -5.9 EQUIVALENT RESISTANCE - COMPUTATION AND ERROR ANALYSIS EMF EQUIVALENT STANDARD DEVIATION GRAD 1 ENT RESISTANCE RESIST COEFFI ANCE CIENT LEVEL 3-4 3-5 2-3 1-4 DIFF. RUN 1 100.9 102.7 4.453 6.651 2.198 0.0017 0.0333 2 88.6 90.3 6.002 8.201 2.199 0.0023 0.0327 3 93.9 95.9 5.264 7.468 2.204 0.0020 0.0327 4 108.5 110.7 3.690 5.892 2.202 0.0015 0.0344 5 118.1 120.3 2.867 5.067 2.200 0.0012 O.O372 REGRESSION COEFFICIENT LEVEL 2-3 LEVEL 1--4 OBSERVED STANDARD DEVIATION 0.027 COMPUTED STANDARD DEVIATION 0 ,0 1 5 0 .0 2 9 TABLE 26A EXPERIMENTAL MEASUREMENTS FLUID - MERCURY-WATER SET THERMOCOUPLE DATA LEVEL RUN 1 2 NO. 3 1 1602.8 1693*7 2 1607*5 1699*8 3 1605*2 1698.8 6 1609*6 1706*0 5 1612.5 1707*7 6 6 1235*5 1265*7 7 1229*0 1258.0 9 1229*1 1258.6 10 1261.8 1273.1 5 11 1620.6 1680.8 13 1622.3 1683*9 16 1626.5 1692.3 15 1623.7 1685*0 1 16 2098.2 2078.5 18 2088.6 2063*6 19 2106.2 2082.6 20 2078.5 2056.7 2 21 2069.0 2063.0 22 2051*8 2022.6 23 2062.0 2012.1 25 2028.7 1998.6 FILM THICKNESS (INCHES) 0 .1 6 1 3 0.1611 EMF, MICROVOLTS 3 6 5 1566.0 1662.5 1536.1 1569.8 1668.1 1539*3 1567.6 1666.5 1536.8 1571*2 1651*0 1560.2 1576.6 1656.3 1 563*6 1223.1 1269*0 1212.9 1217.0 1262.1 1207*1 1217*3 1262.1 1207.6 1229.1 1255*6 1218.5 1396.0 1667.1 1375*8 1397*6 1669*5 1 376.7 1600.9 1669.8 1 376.9 1398.8 1651*0 1378.3 2106.6 2089*8 2113.0 2097*6 2079*8 2106.9 2111.9 2093.5 2120.9 2087.6 2069.0 2095*5 2079*2 2058.3 2087*6 2063*2 2038.5 2072.8 2056.0 2029.5 2063*8 2061.0 2016.1 2051*5 0 .1 7 1 7 0 .1 5 1 8 0.1811 TABLE 26B ANALYSIS OF EXPERIMENTAL DATA FLUID - MERCURY-WATER SET 3 THERMOCOUPLE EMF VS. GRADIENT ANALYSIS LEVEL THERMO EMF WGT. AVG. REGRESSION ZERO COUPLE STANDARD STANDARD COEFF. GRADIENT DEVIATION DEVIATION CORRECTION 3 1 0.167 0.129 1.610 9.5 2 0.371 1.707 3.8 3 0.323 1.757 -3.6 4 0.255 1.812 -5.3 5 0.229 1.820 -2 .8 5 6 0.275 0.131 -1.744 0 .2 7 0.342 -1.804 0.1 9 0.185 -1.804 0.3 10 0.166 - 1.690 0.7 4 11 0.249 1.042 -0.074 6.9 13 0.249 -0.008 1.7 14 2.668 0.176 - 15.2 15 0.374 -0.017 4.1 1 16 0 .32 8 0.438 0.307 -4.4 18 1.067 0.111 6.3 19 1.008 0 .1 8 8 13.8 20 0.253 0.119 -4.3 2 21 0.161 0.150 -0.008 -0.3 22 0.432 -0.205 3.3 23 0.118 -0.237 -2.7 25 0,243 -0.277 - 11.6 EQUIVALENT RESISTANCE - COMPUTATION AND ERROR ANALYSIS EMF EQUIVALENT STANDARD DEVIATION GRADIENT RESISTANCE RESIST COEFFI ANCE CIENT LEVEL 3“** 3-5 2-3 1-4 DIFF. RUN 1 107.9 106.7 4.157 6.244 2.087 0.0027 0.0543 2 126.5 124.8 2.575 4.655 2.080 0.0019 0.0612 3 100.9 99*4 4.956 7.032 2.076 0.0033 0.0539 4 115.4 114.6 3.406 5*500 2.094 0.0023 0.0561 5 94.5 93.6 5.694 7.781 2.087 0 .0038 0.0544 REGRESSION COEFFICIENT LEVEL 2-3 LEVEL 1-4 OBSERVED STANDARD DEVIATION 0.006 O.Otl COMPUTED STANDARD DEVIATION 0.025 TABLE 27A EXPERIMENTAL M EASUREM ENTS FLUID - MERCURY-TOLUENE SET THERM OCOUPLE DATA LEVEL EMF, MICROVOLTS RUN 1 2 3 4 NO, 3 1 1447*8 1365*6 1280.5 1316.1 2 1445*2 1365*3 1279*6 1316.0 3 1 446.0 1 363*2 1 277*6 1 313*6 4 1447*6 1364*8 1278.9 1314.7 5 1450.5 1368.2 1282.1 1318.6 5 6 1182.2 1155*5 1127*8 1139*5 7 1178.9 1153.0 1126.0 1138.0 9 1178*1 1152.6 1125*8 1137*4 10 1187*2 1159*6 1131*1 1143*6 4 11 1312.1 1258.0 1202.8 1225*3 13 1312.5 1258.0 1202.1 1225*0 14 1316.3 1262.0 1205*5 1229*0 15 1311*8 1257*5 1201.5 1224.8 1 16 2124.9 2139*5 2154.8 2146.8 18 2119*3 2135*4 2152.1 2144.0 19 2126.0 2141.0 2156.4 2148.2 20 2115*5 2131*9 2148.7 2140.1 2 21 2095*3 2116.0 2137*5 2126.5 22 2089*9 2112.9 2136.3 2125*1 24 2089*0 2111.9 2135*3 2124*1 25 2078.5 2102.1 2126.8 2115*4 FILM THICKNESS (INCHES) 0 .1 4 2 6 0 .1 5 2 6 0 .1 7 2 2 0 .1 6 2 3 TABLE 27B ANALYSIS OF EXPERIMENTAL DATA FLUID - MERCURY-TOLUENE SET 1 THERMOCOUPLE EMF VS. GRADIENT ANALYSIS LEVEL THERMO EMF WGT. AVG. REGRESSION ZERO COUPLE STANDARD STANDARD COEFF. GRADIENT DEVIATION DEVIATION CORRECTION 3 1 0.021 0.124 1.725 2.2 2 0.201 1.791 -1.5 3 0.143 1.756 -2.0 4 0.058 1.769 -1.4 5 0.407 1.752 2*t 5 6 0.069 0.105 -1.725 -0 .8 7 0.282 -1.778 -0 .0 9 0.154 -1.792 0 .3 10 0.202 -1.678 0 .7 4 11 0.478 0.180 -0.039 0.6 13 0.378 -0.007 -1.4 14 0.147 0.001 2.0 15 0.147 -0.015 -1.5 1 16 0.090 0.080 0.270 -0 .5 18 0.226 0.175 1.1 19 0.141 0.256 1.7 20 0.048 0.169 -2.1 2 21 0.306 0.115 -0.101 -1.8 22 0.111 -0.237 3.2 24 0.083 -0.234 2.0 25 0.241 -0.299 -3.6 EQUIVALENT RESISTANCE - COMPUTATION AND ERROR ANALYSIS EMF EQUIVALENT STANDARD DEVIATION GRADIENT RESISTANCE RESIST COEFFI ANCE CIENT LEVEL 3-4 3-5 2-3 1-4 DIFF. RUN 1 74.8 76.1 8.407 10.615 2.208 0.0056 0.2668 2 59*0 60.1 12.407 14.615 2.209 0.0100 0.3166 3 42.8 43*4 19.675 21.876 2.201 0.0214 0.4195 4 49*1 50.3 16.043 18.260 2.217 0.0152 0.3676 REGRESSION COEFFICIENT LEVEL 2-3 LEVEL 1 -4 OBSERVED STANDARD DEVIATION 0 .1 2 0 0 .1 2 5 COMPUTED STANDARD DEVIATION 0 .1 7 4 TABLE 28A EXPERIMENTAL MEASUREMENTS FLUID - MERCURY-TOLUENE SET 2 THERMOCOUPLE DATA LEVEL EMF, MICROVOLTS RUN 1 2 3 6 5 6 NO. 3 1 1361.6 1360.6 1318.9 1601.3 1670.6 1 586.0 2 1366.0 1362.7 1320.8 1606.6 1675*1 1589*9 3 1360.6 1359.2 1317*3 1600.6 1671.0 1586.9 6 1362.9 1361*6 1319*3 1602*5 1673.6 1586.9 5 1365*7 1363.6 1322*0 1605*0 1675*5 1587.2 5 6 1156.5 1156.0 1160.2 1167*8 1191.2 1228.9 7 1150.6 1150.1 1137*0 1163*6 1186*0 1222.0 9 1151*0 1150.5 1137*3 1163*8 1186*5 1222.6 10 1158.6 1157*8 1163*7 1172*1 1196*3 1236.6 6 11 1258*5 1257.8 1230.1 1286.6 1330*5 1605.0 12 1255.3 1256.5 1226*9 1286*9 1331.8 1606.7 13 1260.1 1259*0 1231*1 1286*6 1333*0 1608.0 15 1260.2 1258.7 1230*8 1285*8 1332*6 1607*5 1 16 2152.1 2152.6 2161.1 2163.6 2128.6 2106.6 18 2166*2 2166.9 2156*5 2136*8 2120.2 2093.6 19 2166.2 2166*3 2172*7 2151*6 2135.9 2112.1 20 2138.5 2139.8 2150.1 2129*6 2112.1 2083*1 2 21 2137*2 2137*5 2168.6 2126*5 2107.8 2077*7 22 2127*1 2127.6 2160.2 2116.5 2093.0 2057*9 23 2120.2 2120.8 2136*2 2107.5 2086.9 2068.3 25 2109*9 2111.2 2125*1 2097*6 2076.6 2036.9 FILM THICKNESS (INCHES) 0 .1 6 1 5 0 .1 6 0 9 0 .1 6 9 7 0 .1 5 6 8 0 .1 6 6 8 0.1390 TABLE 28B 142 ANALYSIS OF EXPERIMENTAL DATA FLUID - MERCURY-TOLUENE SET 2 THERMOCOUPLE EMF VS. GRADIENT ANALYSIS LEVEL THERMO EMF COUPLE STANDARD DEVIATION 3 1 0.355 2 0*255 3 0.165 4 0.172 5 0.429 5 6 0.144 7 0.108 9 0.076 10 0.050 4 11 0.279 12 1.138 13 0.138 15 0.347 1 16 0.324 18 0.168 19 1.459 20 0.562 2 21 0.239 22 0.182 23 0.248 25 0.460 EQUIVALENT RESISTANCE WGT. AVG. STANDARD DEVIATION 0.1 40 REGRESSION ZERO COEFF. GRADIENT CORRECTION 0*054 0.397 0.513 0.161 1*714 1*796 1*765 1*764 1.719 *1.727 *1 *797 ■1*795 •1 *682 •0.048 0.065 -0.008 •0.014 0.328 0*166 0.194 0.098 0.017 •0.210 •0.277 ■0.316 0.9 -1.5 -3.3 - 1.0 4.2 -0.7 -0.4 - 0.1 0.5 2.9 - 6.0 2.0 2.1 -4.5 -0.5 14.3 -3.5 - 0.8 2.6 - 0.1 -7.4 - COMPUTATION AND ERROR ANALYSIS EMF EQUIVALENT STANDARD DEVIATION GRADIENT RESISTANCE RESIST COEFFI ANCE CIENT LEVEL 3-4 3-5 2-3 1-4 DIFF. RUN 1 59*4 59.8 12.746 14.899 2.152 0.0098 0.2926 2 59.1 59.5 12.843 14.996 2.153 0.0099 0.2936 3 51.0 51.4 15.917 18.068 2.151 0.0139 0.3288 4 67.1 67.4 10.540 12.672 2.133 0.0074 0.2699 5 80.4 80.8 7.647 9.785 2.138 0.0048 0.2463 6 101.9 102.7 4.576 6.727 2.151 0.0028 0.2425 REGRESSION COEFFICIENT LEVEL 2-3 LEVEL 1-4 OBSERVED STANDARD DEVIATION 0 .1 4 0 COMPUTED STANDARD DEVIATION 0 .1 1 5 0 .1 3 6 TABLE 29A EXPERIMENTAL MEASUREMENTS FLUID - MERCURY-TOLUENE SET 3 THERMOCOUPLE DATA LEVEL EMF, MICROVOLTS RUN 1 2 3 4 5 6 NO. 3 1 1564.7 1427.1 1390.6 1346.2 1481.9 1481.0 2 1 571*2 1430.5 1 393.1 1348.5 1486.0 1 486.0 3 1 566 . 2 1 427.0 1 389.7 1 345*3 1 482.1 1481.4 4 1569.0 1429.2 1391*5 1347*3 1484.2 1484.1 5 1 5 6 8 .8 1431.2 1 393.8 1 349*5 1485.5 1 484.6 5 6 1257*4 1211.1 1198.5 1183*7 1229*4 1229*7 7 1251.5 1207.0 1195.0 1180.7 1224.8 1225*0 9 1252.4 1207.7 1195.5 1181.2 1225*3 1225*6 10 1261.0 1214.1 1201.5 1186.1 1232*7 1232.7 4 11 1411.5 1 319.8 1 295*8 1 265.9 1 355*7 1 355*9 13 141 3. 3 1 321.3 1 297*8 1 266.9 1 357*5 1 357*6 14 1417*1 1329.2 1 307*4 1 275.8 1 364*5 1 363.9 15 1413.0 1320.9 1296.4 1266.5 1357*3 1357*1 1 16 2122.0 2149.0 2156.4 2165.1 2138.0 2139*1 18 2110.1 2141.0 2149.0 2159.5 2128.1 2129*6 19 2123.3 2151.0 2158.9 2167.5 2140.0 2140.8 20 2100.5 2133.9 2143*0 2153*8 2120.2 2121.0 2 21 2096.5 2131*9 2141.8 2152.8 2117*7 2118.5 22 2079.6 2121.4 2132*8 2146.0 2104.9 2105*5 23 2 0 7 0 .8 2114.4 2125*5 2140.5 2097*1 2098.0 25 2059.5 2104*4 2117*2 2131.6 2086*5 2087*3 FILM THICKNESS (INCHES) 0 .1 3 7 9 0 .1 5 1 7 0 .1 5 8 4 0 .1 6 8 0 0 .1 4 5 2 0 .1 4 5 2 TABLE 29B ANALYSIS OF EXPERIMENTAL DATA FLUID - MERCURY-TOLUENE SET 3 THERMOCOUPLE EMF VS. GRADIENT ANALYSIS 144 LEVEL THERMO EMF WGT• AVG. REGRESSION ZERO COUPLE STANDARD STANDARD COEFF. GRADIENT DEVIATION DEVIATION CORRECTION 3 1 0.178 0.132 1.716 -0.7 2 0.338 1.820 -3.7 3 0.202 1.775 -4.6 4 0.362 1.797 -3.8 5 0.296 1.734 1.7 5 6 0.225 0.103 - 1.708 -2.7 7 0.213 -1.775 -2.5 9 0.223 -1.767 -2.4 10 0.116 -1.683 -1.3 4 11 0.216 0.384 -0.015 0 .2 13 0.413 -0.002 1 .0 14 1.049 -0.134 17.0 15 0.040 o.oto “0.4 1 16 0.102 0.104 0.325 -2 .2 18 0.292 0.179 -1 .2 19 0.172 0.297 1.7 20 0.163 0.080 -2.1 2 21 0.169 0.133 0.008 0.5 22 0.172 -0.228 4.8 23 0.379 -0.295 1.9 25 0.218 -0.365 -3.4 EQUIVALENT RESISTANCE - COMPUTATION AND ERROR ANALYSIS EM F G R A D I EN T EQUIVALENT RESISTANCE LEVEL 3-4 3-5 2-3 1-4 DIFF. RU N 1 86.0 89.2 5*666 7.910 2.244 2 60.3 62.5 10.966 13.212 2.246 3 54.0 55.4 13.249 15.477 2.228 4 45.0 47.0 16.871 19*127 2.256 5 70.5 73.1 8.409 10.651 2.242 6 70.3 72.9 8.450 10.697 2.246 REGRESSION COEFF ICIENT LEVEL 2-3 STANDARD DEVIATION RESIST- COEFFI — ANCE Cl ENT OBSERVED STANDARD DEVIATION 0 .0 8 0 COMPUTED STANDARD DEVIATION 0 .1 2 7 0.0037 0.0009 0.0119 O.OI77 0.0061 0.0061 LEVEL 1-4 0 .0 8 5 0.2544 0.3087 0.3394 0.3911 0.2778 0.2783 TABLE 30A EXPERIMENTAL MEASUREMENTS FLUID - GLYC.-TOLUENE SET THERMOCOUPLE DATA LEVEL RUN I 2 NO* 3 1 1146*6 1165.2 2 1144.6 1163.1 3 1143.5 1161.6 4 1145.0 1163*1 5 1147*4 1165.6 5 6 1030.3 1036.3 7 1024.8 1030.7 8 1028.0 1033.6 10 1030.5 1036.7 4 11 1092.2 1104.6 13 1090.5 1102.6 14 1089*7 1101.9 15 1089*8 1102.0 1 16 2157*7 2155*1 17 2162.4 2159*8 18 2159*7 2157*3 20 2152.3 2149*8 2 21 2144.1 2141*1 22 2135*4 2131*4 23 2146.1 2142.7 24 2141.4 2138.1 FILM THICKNESS (INCHES) 0.1014 0.0917 EMF, MICROVOLTS 3 4 5 1189*0 1220.9 1263*5 1187*6 1219*3 1262.0 1185*8 1217*1 1259*3 1187*2 1218.3 1260.4 1190.0 1220.9 1262.6 1043.8 1053.9 1067.4 1038.3 1048.0 1061.1 1040.9 1050.5 1063*6 1044.6 1055*0 1069.0 1120.3 1141.2 1169*0 111.8.5 1139.1 1167*0 1118.0 1138.3 1166.0 1118.0 1138.3 1165*8 2152.6 2147.4 2141*7 2157*6 2152.5 2147*8 2155*1 2149.7 2144*9 2147*2 2141.3 2135*8 2137 * 8 2131.1 2124.5 2126.2 2117*6 2107.6 2138.4 2130.6 2122.2 2133*5 2125.4 2116.6 0.0816 O.O717 0.0613 TABLE JOB ANALYSIS OF EXPERIMENTAL DATA FLUID - GLYC.-TOLUENE SET 1 THERMOCOUPLE EMF VS. GRADIENT ANALYSIS LEVEL THERMO EMF WGT* AVG. REGRESSION ZERO COUPLE STANDARD STANDARD COEFF. GRADIENT DEVIATION DEVIATION CORRECTION 3 1 0.252 0.082 1.784 -1.2 2 0.019 1*809 -4.0 3 0.091 1.741 -2.9 4 0.076 1.721 -0.7 5 0.196 1.712 2.2 5 6 0.072 0.042 -1.739 0.2 7 O.O75 -1*775 -4.0 9 0.111 -1*804 o.o 10 0.023 -1*677 -1.6 4 11 0.124 0.067 0.013 3*7 13 0.045 0*001 2.3 14 0.149 -0.010 2.0 15 0.151 -0.023 2.6 1 16 0.184 0.085 0.174 1.9 17 0.218 0.234 4*4 18 0.119 0,220 2.4 20 O.O75 0*142 -2.3 2 21 0.075 0.077 0*005 -6.0 22 0.143 -0.357 -2.4 23 0.106 -0.187 2.6 24 0.213 -0.231 -0.5 EQUIVALENT RESISTANCE - COMPUTATION AND ERROR ANALYSIS EMF EQUIVALENT STANDARD DEVIATION GRADIENT RESISTANCE RESIST COEFFI ANCE CIENT LEVEL 3-4 3-5 2-3 1-4 DIFF. RUN 1 33*1 33.4 29*824 31.978 2.153 0.0237 0.3116 2 36.6 36.9 26.384 28.520 2.136 0.0190 0.2918 3 41.4 41.7 22.696 24.834 2.139 0.0146 0.2740 4 47.4 47.8 18.972 21.114 2.142 0.0107 0.2619 5 55*5 56.0 15*280 17*425 2.145 0.0074 0.2601 REGRESSION COEFFICIENT LEVEL 2-3 LEVEL 1-4 OBSERVED STANDARD DEVIATION 0.064 0.060 COMPUTED STANDARD DEVIATION 0.125 TABLE 31A EXPERIMENTAL MEASUREMENTS FLUID - GLYC.-TOLUENE SET THERMOCOUPLE DATA LEVEL EMF, MICROVOLTS RUN 1 2 3 A 5 NO* 3 1 1190.5 1172.1 1312.0 12A2.8 1215*1 2 1189.0 1170. I 1311.3 1241.6 1213*7 3 1188.7 1170.1 1310.0 12A0.9 1213*1 A 1190.1 1171*3 1311.5 12A2.3 121A.5 5 1192.1 1173.0 1312.8 12AA.0 1216.5 5 6 106A.2 1057.8 110A.1 1081.3 1072.1 7 1060.2 105A.5 1099*A 1077.5 1068.8 9 1062.2 1055*7 1100*5 1078.5 1069*9 10 1065.A 1059*1 1106.8 1083.A 107A.1 A 11 1129*9 1117*7 1209*5 1163*6 1145*5 13 1128.9 1116.0 1209.5 1163*5 11A5*0 1A 1128.8 1116*0 1208.7 1162.7 11AA.5 15 1129.2 1116.6 1209.A 1163*5 11A5.1 1 16 2157*0 2159*6 2138.1 21A9.0 2153.5 18 2160.1 2162.A 21A2.5 2152.6 2156.9 19 2161.5 216A.0 21AA.6 215A.3 2158.3 20 2153*8 2156.5 2133*6 21A5.2 2150.0 FILM THICKNESS (INCHES) 0 .0 9 1 A 0 .1 0 1 9 0 .0 5 6 0 0 .0 7 1 5 0 .0 8 1 2 TABLE 51B ANALYSIS OF EXPERIMENTAL DATA FLU 10 - GLYC.-TOLUENE SET 2 THERMOCOUPLE EMF VS. GRADIENT ANALYSIS LEVEL THERMO EMF WGT. AVG. REGRESSION ZERO COUPLE STANDARD STANDARD COEFF. GRADIENT DEVIATION DEVIATION CORRECTION 3 1 0.170 0.071 1.750 -0.2 2 0.087 1.793 -3.4 3 0.092 1.748 -2.0 4 0.050 1.756 -1.0 5 0.230 1.735 1.6 5 6 0.100 0.107 -1.733 -O.A 7 0.311 -1.777 -2.3 9 0.164 -1.795 -0.3 10 0.145 -1.677 -1.0 A 11 0.334 0.119 -o.o4i 3.9 13 0.133 0.017 0.7 14 0.221 -0.01A 1.6 15 0.112 -0.006 1.9 1 16 0.583 0.291 0.210 -0.8 18 0.557 0.268 0.2 19 0.634 0.291 0.8 20 0.546 0.157 -2.1 2 21 0.639 1.441 -0.070 -2.9 23 0.541 -0.164 1.4 24 0.483 -0.219 0.0 25 3.877 -0.473 3.5 EQUIVALENT RESISTANCE - COMPUTATION AND ERROR ANALYSIS EMF EQUIVALENT STANDARD DEVIATION GRADIENT RESISTANCE RESIST COEFFI ANCE CIENT LEVEL 3-4 5-5 2-3 1-4 DIFF. RUN 1 35.9 56.3 26.245 28.424 2.179 O.OA79 0.6593 2 32.3 32.7 29.737 31.997 2.260 0.0554 0.6707 3 58.8 59.6 13.419 15.646 2.227 0.0256 0.7063 k 45.5 46.3 19.130 21.371 2.241 0.0347 0.6629 5 40.2 40.9 22.481 24.726 2.246 O.0A06 0.6569 REGRESSION COEFFICIENT LEVEL 2-5 LEVEL 1-4 OBSERVED STANDARD DEVIATION 0.128 0.108 COMPUTED STANDARD DEVIATION 0 .5 0 0 TABLE 32A EXPERIMENTAL MEASUREMENTS FLUID - GLYC.-TOLUENE SET THERMOCOUPLE DATA LEVEL EMF, MICROVOLTS RUN 1 2 3 4 5 NO. 3 1 1203.5 1235.0 1259.6 1284.6 1331*9 2 1206.4 1238.0 1259*7 1287*4 1332.3 3 1200.6 1232.0 1253.4 1280.6 1327.9 4 1201.2 1232.1 1253.6 1280.1 1327.2 5 1202.5 1232.5 1253*5 1279.5 1325.5 5 6 1102.3 1112.5 1119.4 1127*4 1145*1 7 1099*3 1109.1 1116.0 1123.2 1138.5 9 1101.4 1111.7 1118.4 1125.2 1143.0 10 1102.8 1113.6 1120.8 1128.6 1147.4 4 11 1153.6 1174.6 1188.8 1205*5 1239*5 13 1152.5 1173.3 1187.6 1204.1 1237*0 14 1153.8 1173*9 1188.0 1205*0 1233.8 15 1151.0 1171*4 1185*0 1201.9 1232.2 1 16 2168.3 2163.0 2158.5 2152.4 2144.0 18 2165.5 2159.2 2154.4 2147.2 2138.3 19 2169.0 2163*1 2158.6 2151*9 2144.4 20 2163.0 2155.8 2150.6 2143.0 2134.6 2 21 2159.0 2152.3 2147.5 2140.9 2132.8 22 2155.8 2147.4 2141.1 2132.3 2119.8 23 2154.4 2145.5 2139.1 2129.8 2117.1 25 2147.9 2139.0 2132.4 2122.6 2108.9 FILM THICKNESS (INCHES) 0 .1 2 1 5 0.1 01 7 0 .0 9 1 5 0 .0 8 1 6 0.0717 TABLE 32B ANALYSIS OF EXPERIMENTAL OATA 150 FLUID - GLYC.-TOLUENE SET 3 THERMOCOUPLE EMF VS, GRADIENT ANALYSIS LEVEL THERMO EMF WGT, AVG, REGRESSION ZERO COUPLE STANDARD STANDARD COEFF. GRADIENT DEVIATION DEVIATION CORRECTION 3 1 1.073 0,321 1.860 -2.3 2 0.719 1.770 3.2 3 0,411 1.814 -4.5 4 0.377 1.759 -2.3 5 0,400 1.638 2.4 5 6 0,218 0.192 - 1.698 - 1.1 7 0.557 -1.843 0.6 9 0,293 -1.762 0.1 10 0,254 - 1.632 -2.4 4 11 0,692 0,316 0.078 -1.3 13 0.387 0.024 -0.6 14 0,817 -0.139 15 0,325 -0.101 1.8 1 16 0,255 0.170 0.253 0.8 18 0,080 0,130 1.5 19 0,252 0.236 1.7 20 0.477 0.079 -O’ .O 2 21 0,370 0.168 0.178 -6.9 22 0.253 -0.231 2.3 23 0.160 -0.286 2.4 25 0.424 -0.359 -1.7 EQUIVALENT RESISTANCE - COMPUTATION AND ERROR ANALYSIS EMF EQUIVALENT STANDARD DEVIATION GRADIENT RESISTANCE RESIST COEFFI LEVEL 3-4 3-5 RUN 2-3 1-4 DIFF. ANCE CIENT 1 27.9 29.0 32.872 35.029 2,158 0,1219 1.3297 2 33.8 34.9 26,148 28,299 2.150 0,0807 1.1096 3 37*8 39,2 22,554 24.704 2.150 0.0621 0.9931 4 43.1 44.6 19.023 21.167 2.144 0.0462 0.8804 5 51.1 53.0 14.935 17.092 2.156 0.0309 0.7567 REGRESSION COEFFICIENT LEVEL 2-3 LEVEL 1-4 OBSERVED STANDARD DEVIATION 0 ,2 9 6 COMPUTED STANDARD DEVIATION 0 ,4 6 2 0,291 TABLE 33A EXPERIMENTAL MEASUREMENTS FLUID - WATER-NUJOL SET THERMOCOUPLE DATA LEVEL EMF, MICROVOLTS RUN I 2 3 A 5 NO. 3 1 1218.7 1235.2 1245.5 1 257.** 1270.7 2 1217.5 1233.1 124*4.2 1256.6 1269.1 3 1217*4 1233.9 1244.4 1256.1 1269.0 4 1218.0 1235.6 1245.8 1257*3 1270.6 5 1219.8 1237.5 1248.1 1259.5 1273.0 5 6 1110.0 1115.7 1118.9 1122.9 1127.1 7 1104.5 1110.0 1113.2 1117.4 1121.6 8 1105.6 1110.5 1114.0 1118.1 1122.0 10 1110.2 1116.6 1119.8 1123.9 1128.4 4 11 1164.8 1175.6 1182.4 1189.9 1198.5 13 1164.3 1174.5 1181.6 1188.9 1197.4 14 1162.8 1173.8 1180.6 1188.1 1197*1 15 1162.9 1173.5 1180.2 1187.3 1195*4 1 16 2167.0 2163.0 2161.0 2158.9 2156.4 18 2164.4 2160.2 2157*5 2155*8 2152*7 19 2167.0 2163*6 2161.4 2159.4 2157*0 20 2160.4 2157.0 2154.0 2152.0 2149.0 2 21 2154.4 2149*5 2146.3 2143.5 2140.0 22 2153.6 2148.3 2145.4 2142.2 2138.5 23 2153.0 2147.4 2144.5 2141.3 2137*4 25 2146.1 2140.6 2137-5 2134.0 2129.9 FILM THICKNESS (INCHES) 0 .1 6 1 5 0 .1 5 1 8 0 .1 4 6 2 0 .1 4 1 5 0 .1 3 6 6 TABLE 33B ANALYSIS OF EXPERIMENTAL DATA FLUID - WATER-NUJOL SET 1 THERMOCOUPLE EMF VS. GRADIENT ANALYSIS 152 LEVEL THERMO EMF WGT• AVG. REGRESSION ZERO COUPLE STANDARD DEVIATION STANDARD DEVIATION COEFF. GRADIENT CORRECT 1C 3 1 0.208 0.181 1.773 -0.7 2 0.578 1.786 -2.6 3 0.073 1.740 1.809 -0.8 4 0.357 -2.0 5 0.352 1.871 -2.2 5 6 0.595 0.370 -1.735 -1.2 7 0.097 -1.714 -4.5 8 0.238 -1.767 -1.9 10 0.2 37 0.088 -1.623 -1.5 4 11 0.060 -0.060 3.5 13 0.225 -0.109 4.4 14 0.173 -0.010 -0.1 15 0.155 -0.179 5.5 1 16 0.127 0.102 0.256 0.5 18 0.117 0.154 1.3 19 0.086 0.305 -0.8 20 0.302 0.159 -2.7 2 21 0.107 0.060 -0.133 0.4 22 0.093 -0.196 1.5 23 0.142 -0.239 2.2 25 0.126 -0.306 -2.4 EQUIVALENT RESISTANCE - COMPUTATION AND ERROR ANALYSIS EMF GRADIENT EQUIVALENT RESISTANCE LEVEL 3-4 3-5 2-3 1-4 DIFF. RUN 1 29.1 31.6 29.464 31.784 2.319 2 31.9 34.8 26.132 28.460 2.329 3 33.9 36.9 24.294 26.609 2.315 4 35.8 39.1 22.547 24.874 2.327 5 38.3 41.6 20.764 23.083 2.320 STANDARD DEVIATION RESIST- COEFFI- ANCE ClENT 0.0553 0.6543 0*0447 0.5965 0.0392 0.5645 0.0344 0.5345 0.0298 0.5039 REGRESSION COEFFICIENT LEVEL 2-3 LEVEL 1-4 OBSERVED STANDARD DEVIATION 0 .0 8 2 COMPUTED STANDARD DEVIATION 0 .2 5 6 0.081 TABLE 34A EXPERIMENTAL MEASUREMENTS FLUID - WATER-NUJOL SET THERMOCOUPLE DATA LEVEL EMF, MICROVOLTS RUN 1 2 3 4 $ NO* 3 1 1254.9 1268.0 1240.9 1226.2 1216.6 2 1254.0 1267.0 1240.1 1225.4 1216.0 3 1252.6 1265*5 1238.3 1224.1 1214.4 4 1253.9 1266.5 1239.3 1225*2 1215.8 5 1255*8 1268.4 1241.2 1226*9 1217*4 5 6 1117.8 1122.0 1111.6 1107.0 1103.9 7 1115.2 1119.3 1109.8 1105*3 1102.5 9 1115.8 1119*8 1110.0 1105.4 1102.5 10 1120.1 1124.2 1113.7 1108.9 1105*9 4 11 1186.8 1199.1 1177*5 1168.0 1161.9 12 1188.0 1196.4 1177*8 1168.4 1162.0 15 1187.9 1196.3 1177*9 1168*5 1162.2 1 16 2161.5 2159.0 2159.1 2161.5 2163.1 18 2162.1 2160.0 2158.9 2161.1 2162.7 19 2164.5 2162.4 2162.6 2164.6 2165-9 20 2157*1 2154.9 2154.4 2157*0 2159.0 2 21 2146.2 2143.1 2144.9 2148.3 2150.8 22 2146.6 2143.0 2144.6 2148.2 2150.5 24 2145.5 2142.0 2144.1 2147*8 2150.1 25 2137.3 2133*5 2136.7 2140.6 2143*3 FILM THICKNESS (INCHES) 0 .1 3 1 8 0 .1 2 7 0 0 .1 3 6 9 0 .1 4 3 6 0 .1 4 9 2 TABLE 3AB ANALYSIS OF EXPERIMENTAL DATA FLUID - WATER-NUJOL SET 2 THERMOCOUPLE EMF VS* GRADIENT ANALYSIS LEVEL THERMO EMF WGT. AVG. REGRESSION ZERO COUPLE STANDARD STANDARD COEFF. GRADIENT DEVIATION DEVIAT ION CORRECTION 3 1 0.127 0.067 1.799 -1.7 2 0.1 A8 1.762 -1.2 3 0.093 1.765 -2.8 A 0.191 1.7A1 -0.7 5 0.155 1.77A -0.1 5 6 0.091 0.058 -1.686 -2.6 7 0.120 -1.830 0.6 9 0.025 -1.768 -1.A 10 0.1 A2 -1.652 -1.8 A 11 0.202 0.009 -0.111 A.9 12 0.07A 0.021 0,8 15 0.032 -0.012 2.0 1 16 0.067 0.117 0.19A 1.3 18 0.207 0.352 -A.A 19 0.289 0.239 2.8 20 0.2A1 0.200 -3.3 2 21 0.110 0.07A -0.188 1.1 22 0.187 -0.152 -0.3 2A O.O75 -0.231 1.9 25 0.165 -0.A12 0.9 EQUIVALENT RESISTANCE -■ COMPUTATION AND ERROR ANALYSIS EMF EQUIVALENT STANDARD DEVIATION GRADIENT RESISTANCE RESIST COEFFI ANCE CIENT LEVEL 3-A 3-5 2-3 1-A DIFF. RUN 1 37.8 39.1 22.682 2A.978 2.295 0.01A9 0.25A5 2 AO. 2 A1.6 20.930 23*225 2.296 0.0130 0.2A29 3 35.6 36.7 2A.503 26.793 2.290 0.0171 0.2675 A 32.8 3A.0 27.0A9 29.3A1 2.292 0.020A 0.2856 5 30.9 32.1 29.00A 31.303 2.299 0.0231 0.2998 REGRESSION COEFFICIENT LEVEL 2-3 LEVEL 1-1* OBSERVED STANDARD DEVIATION O.OA5 0.01*5 COMPUTED STANDARD DEVIATION 0.121 TABLE 35A EXPERIMENTAL MEASUREMENTS FLUID - WATER-NUJOL SET THERMOCOUPLE DATA LEVEL EM F,, M ICROVOLTS RU N 1 2 3 4 5 NO, 3 1 1240.1 1253.0 1267.0 1284.0 1300.5 2 1245*0 1257.9 1272.0 1289.4 1306.3 3 1239.0 1251.6 1265*5 1283.0 1299.6 4 1240.5 1253.2 1267.0 1284.6 1301.4 5 1241.9 1254.6 1268.4 1286.1 1302.9 5 6 1147*3 1152.0 1156.1 1162.0 1166.3 7 1145.9 1150.1 1154.2 1159.7 1163.8 9 1146.4 1150.6 1155*0 1160.4 1164.8 10 1148.4 1153.0 1157.4 1163.2 1167.8 4 11 . in a \ 1204.2 1213.1 1224.6 1234.6 13 1196.5 1205.2 1214.3 1226.0 1238.9 1A 1199.8 1208.5 1217*4 1228.8 1238.3 15 1194.9 1203.8 1212.6 1224.2 1234.4 1 16 2187.7 2185.6 2182.4 2178.7 2174.1 18 19 2184.9 2189.2 2182.4 2187.1 2179.1 2184.0 2175.0 2180.5 2169.9 2176.2 20 2180.5 2178.0 2174.1 2169.9 2164.6 2 21 2180.1 2177.6 2173.6 2169.0 2163*4 22 2176.3 2173.2 2168.5 2163.3 2157.0 23 2173.0 2169.8 2164.7 2159.3 2152.4 25 2165.9 2162.5 2156.9 2151.3 2144.1 F ILK THICKNESS (INCHES) 0.1 61 1 0 .1511 0.11*13 0 .1 3 1 3 0 .1 2 1 5 TABLE 35B ANALYSIS OF EXPERIMENTAL DATA FLUID - WATER-NUJOL SET 3 THERMOCOUPLE EMF VS. GRADIENT ANALYSIS LEVEL THERMO EMF WGT• AVG. REGRESSION ZERO COUPLE STANDARD STANDARD COEFF. GRADIENT DEVIATION DEVIATION CORRECTION 3 1 0.191 0.059 1*704 -0.6 2 0.069 1.782 2.1 3 0.099 1.734 “2*I 4 0.103 1.755 -1.8 5 0.127 1.765 -0.7 5 6 0.098 0.050 -1.730 -1.0 7 0.072 -1.815 -0.3 9 0.130 -1.775 -0.8 10 0.023 -1.696 -0.9 4 11 0.294 0.262 -0.032 1.3 13 0.769 0.186 -3.9 14 0.338 -0.101 7.8 15 0.162 -0.029 0.9 1 16 0.064 0.055 0.282 0.4 18 0.143 0.173 0.5 19 0.117 0.333 0.4 20 0.038 0.091 -1.7 2 21 0.084 0.061 0.020 -0.0 22 0.030 -0.194 1.8 23 0.110 -0.301 1.5 25 0.167 -0.403 -2.9 EQUIVALENT RESISTANCE - COMPUTATION AND ERROR ANALYSIS EMF EQUIVALENT STANDARD DEVIATION GRADIENT RESISTANCE RESIST COEFFI ANCE CIENT LEVEL 3-4 3-5 2-3 1-4 DIFF. RUN 1 26.9 26.9 34.599 36.788 2.189 0.0286 0.2749 2 29.4 29.3 31.250 33.420 2.170 0.0238 0.2553 3 32.0 32.1 27.974 30.159 2.185 0.0195 0.2368 4 35.4 35.4 24.677 26.858 2.181 0.0156 0.2190 5 39.0 39.0 21.844 24.027 2.182 0.0126 0.2049 REGRESSION COEFFICIENT LEVEL 2-3 LEVEL 1--4 OBSERVED STANDARD DEVIATION 0.164 0.166 COMPUTED STANDARD DEVIATION 0 .1 0 7
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Asset Metadata
Creator
Cooper, Harrison Raymond
(author)
Core Title
An Experimental Investigation Of Heat Conduction Through Liquid-Liquid Phase Boundaries
Degree
Doctor of Philosophy
Degree Program
Chemical Engineering
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
engineering, chemical,OAI-PMH Harvest
Format
dissertations
(aat)
Language
English
Contributor
Digitized by ProQuest
(provenance)
Advisor
Lockhart, Frank J. (
committee chair
), Edwards, Richard H. (
committee member
), Lenoir, John M. (
committee member
), Rebert, Charles J. (
committee member
)
Permanent Link (DOI)
https://doi.org/10.25549/usctheses-c18-296566
Unique identifier
UC11359087
Identifier
6402567.pdf (filename),usctheses-c18-296566 (legacy record id)
Legacy Identifier
6402567.pdf
Dmrecord
296566
Document Type
Dissertation
Format
dissertations (aat)
Rights
Cooper, Harrison Raymond
Type
texts
Source
University of Southern California
(contributing entity),
University of Southern California Dissertations and Theses
(collection)
Access Conditions
The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the au...
Repository Name
University of Southern California Digital Library
Repository Location
USC Digital Library, University of Southern California, University Park Campus, Los Angeles, California 90089, USA
Tags
engineering, chemical